I want to make this as simple as possible, so I will start by explaining reasoning first.
Reasoning usually comes in form of premises and conclusion.
Deductive reasoning is more logically accurate, but it can be based on assumptions.
Example:
Premise 1:
If it rains today, I will bring an umbrella.
Premise 2:
It rains today.
Conclusion:
I will bring an umbrella.
We see that as long as premise 1 and premise 2 are true, conclusion logically follows.
So is this reasoning based on facts?
No, not even close.
This is because none of the premises are proven to be true.
Premise 2 is an assumption.
There is no proof it rains today.
Premise 1 is an assumption too.
There is no proof that I will bring an umbrella if it rains.
It is not disproven that it rains today and I wont bring an umbrella because I forgot and was in a rush, or maybe I just like walking in rain without an umbrella, or it didnt rain much and I figured I wouldnt need it.
So since every premise is essentially unproven assumption, this reasoning is based on assumptions.
The other form of reasoning, without the use of "if" would be inclusion, category reasoning.
Premise 1:
I will bring an umbrella on days when it rains.
Premise 2:
It rains today.
Conclusion:
I will bring an umbrella today.
Despite changing from "if" to inclusion, it still stands that every premise is an assumption.
The claim "I will bring an umbrella" is included in category "on days when it rains".
But this inclusion is an assumption.
It could be possible that there are days when it rains and I dont bring an umbrella, therefore making the premise an assumption.
Since its not proven that I will bring an umbrella on days when it rains, the premise is essentially unproven.
Another form of reasoning is options reasoning, which is "this or that".
Example:
Premise 1:
It wont rain
or
I will bring an umbrella.
Premise 2:
It rains.
Conclusion:
I will bring an umbrella.
Since "or" in this reasoning means that when one option is true, the other is false,
when "it wont rain" is false, then "I will bring an umbrella" is true.
But premise 1 is still an assumption, because both options can be true.
It can be true both that "it wont rain" and that "I will bring an umbrella", since people can obviously bring an umbrella even on days it doesnt rain.
Also, they can both be false.
It can be false that it "it wont rain" and it can at the same time be false that "I will bring an umbrella".
So what is reasoning based on facts?
Its reasoning where every premise is a fact.
Example:
Premise 1:
Sun exists.
or
It is false that Sun exists.
Premise 2:
Sun exists
Conclusion:
The claim "It is false that Sun exists" is not true.
Premise 1 is a fact, since Sun can logically either exist either not exist, but not both and not neither.
Premise 2 is a fact, since Sun is observable to exist.
Conclusion then logically follows.
So, reasoning based on facts is reasoning where every premise is an observable fact, and conclusion logically follows from true premises.
This reasoning uses "if" premise when that premise can be observed.
For example, when we observe that "if there is source of light, there will be light".
It uses inclusion when inclusion can be observed.
Example:
"Not all dogs have tail"
It uses "or" when logically, options are presented which cant all be true,
where one of them must be true, where all except one are false,
where there are no other options, such as Sun which either exists either doesnt.
That is reasoning where every premise is an observable fact.