It's not. Using tools can be purely bodily, a cat's claw is a tool that it uses everyday. Using tools can be a purely bodily function.
Problem-solving isn't innately abstract either. An example of problem-solving that doesn't involve abstraction is a worm in some dirt that gets stuck in front of a rock, it wraps around the rock and moves past it. Problem solved, using just it's bodily senses
If only I had 10€ each time someone was telling me "I don't agree" in front of scientific evidences....
How can a material (cerebrum) cause an immaterial (abstraction) effect?
Through complex cognitive processes : Memory/recognition pattern/Language recognition and capacity etc.
> Each of those process are determined by neurobiological mechanisms, neural network and cognitive development.
>> Each of those mechanism are determined by genetic predisposition and the experience of our material condition of existence in and outside of the brain.
>>> Which is determined by our evolution
>>>> Which is determined by the material condition of existence of the livings (Earth and it's components / The sun / The moon)
>>>>> Which is the result of the creation of the solar system
>>>>>> Which was formed after the creation of the Sun from a Nebulae
>>>>>>> Which is the result a chain of reaction created by the explosion of a supernovae
>>>>>>>> Which was the result of a chain of event following the creations of stars and galaxies
>>>>>>>>> Which were formed with by the matter in the universe under the influence of gravity
>>>>>>>>>> Which emerged following the big bang
>>>>>>>>>>> Which was determined by a few fundamental physical constant
>>>>>>>>>>>> Which are the results of a chain of causality created by the existence of the universe
>>>>>>>>>>>>> Which is a result of ?
By thinking that you have free will, you negate all of that, bypassing the chain of causality in the universe and attributing yourself the power of a god.