The nature of intellectual reasoning in the Qur’an

Does the Qur'an invite us to think, and use our intellectual reason to think?
Allah ﷻ encourages Muslims to reflect, think and pondering over the creation of Allah ﷻ, Quran, 38:29 reads:(This is a) Book that We have sent down to you, full of blessings, so that they may ponder over its verses, and that men of understanding may remember.
From the verse above “that they may ponder over its verses” from this beautiful verse, we understand from it that using our intellectual thinking over the verses, signs and creation of Allah is part of what Qur'an permits us.
Allah mentioned in many places in the Quran where we can freely apply our intellectual thinking in Islam without restriction in other to ponder and know the greatness of Allah the most High.
When it comes to thinking in Islam, there are some aspects we are allowed and some we are not to use and apply our intellectual thinking which we have numerous verses affirming this.
Qur'an 13:19 reads:
“Then is he who knows that what has been revealed to you from your Lord is the truth like one who is blind? They will only be reminded who are people of understanding.”
Qur'an 13:19 reads
“Then is he who knows that what has been revealed to you from your Lord is the truth like one who is blind? They will only be reminded who are people of understanding.”
Qur'an 88:17,18,19 and 20 read:
“Then do they not look at the camels - how they are created?”
“And at the sky how it is raised”
“And at the mountains how they're erected”
“And at the earth, how it is spread out”
It's obviously clear that using our intellectual thinking is highly recommended.
But thinking other than what Qur'an has brought to us  is not accepted in Islam, Allah says in Quran chapter 4;82
أَفَلَا يَتَدَبَّرُونَ ٱلۡقُرۡءَانَۚ وَلَوۡ كَانَ مِنۡ عِندِ غَيۡرِ ٱللَّهِ لَوَجَدُواْ فِيهِ ٱخۡتِلَٰفًا كَثِيرًا
Then do they not reflect upon the Qur’ān? If it had been from [any] other than Allāh, they would have found within it much contradiction.
Allah commands them to contemplate about the Qur'an and forbids them from ignoring it, or ignoring its wise meanings and eloquent words.
Allah states that there are no inconsistencies, contradictions, conflicting statements or discrepancies in the Qur'an, because it is a revelation from the Most-Wise, Worthy of all praise. Therefore, the Qur'an is the truth coming from the Truth, Allah.

Firstly,what is philosophical ways of inquiries and religious ways of inquiries
Philosophical ways of inquiry are methods of exploring and analyzing ideas and concepts using logic and critical thinking it involves evaluating different argument identifying and accessing evidence and coming to well reasoned conclusions.
While, Religious ways of inquiry are method of exploring and understanding the world and place in it through the lens of a particular religious tradition this can include studying sacred texts,Engaging in spiritual practice and reflecting on the textings and wisdom of religious leaders and philosophers. Religious inquiry often involves an elementof faith and a belief in the existence of a higher power o divine being. This can take the form of prayer ,meditation,and other spiritual practice that aim to connect the individual with a higher power the goal of religious inquiry is often to final meaning and purpose in life and to connect with something greater than oneself.
Secondly,Which one solve our problem better it depends on the individual and the specific problem ones trying to solve in general. Philosophical inquiry tends to be more holistic and intuitive so for example if you are trying to solve a scientific or mathematical problem a philosophical approach may be more effective on the other hand, if you are dealing with a more emotional or existential issue a religious approach may be more helpful. The important things is to find the approach that best fits the particular problems ones facing.
Thirdly, which of the two satisfactory address fundamental human concern
Both philosophical and religious inquiry can address fundamental human concern but philosophical way is more satisfactory address fundamental human concern because it tend to be more focused on rational thinking and logical analysis and more effective in addressing IB issues such as morality, knowledge and the existence of a higher power and it help us to understand the world around us and to find solution to problems.

1st Question:
Does the Quran invite us to think and use our intellectual reasoning to think?
Q13:3

﴿وَهُوَ الَّذي مَدَّ الأَرضَ وَجَعَلَ فيها رَواسِيَ وَأَنهارًا وَمِن كُلِّ الثَّمَراتِ جَعَلَ فيها زَوجَينِ اثنَينِ يُغشِي اللَّيلَ النَّهارَ إِنَّ في ذلِكَ لَآياتٍ لِقَومٍ يَتَفَكَّرونَ﴾ [Ar-Ra‘d: 3]
(3) And it is He who spread the earth and placed therein firmly set mountains and rivers; and from all of the fruits He made therein two mates; He causes the night to cover the day. Indeed in that are signs for a people who give thought.

*Allah has referred to the philosophers and the wise ones as hulul_Albal in Q1:269 which means Almighty Allah Want us to think and he appreciates and acknowledges those with intellectual reasoning



﴿يُؤتِي الحِكمَةَ مَن يَشاءُ وَمَن يُؤتَ الحِكمَةَ فَقَد أوتِيَ خَيرًا كَثيرًا وَما يَذَّكَّرُ إِلّا أُولُو الأَلبابِ﴾ [Al-Baqarah: 269]
(269) He gives wisdom[108] to whom He wills, and whoever has been given wisdom has certainly been given much good. And none will remember except those of understanding.
[108]- The knowledge and understanding of the religion and of the Qur’ān.