
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Find all nonzero subsets  $A$  of the set  $\left\{2,3,4,5,\cdots\right\}$  such that  $\forall n\in A$ , we have that  $n^{2}+4$  and  $\left\lfloor{\sqrt{n}\right\rfloor}+1$  are both in  $A$ .

Present the answer in LaTex format: \boxed{Your answer}
user