
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 prime numbers  $p$  which satisfy the following condition: For any prime  $q < p$ , if  $p = kq + r, 0 \leq r < q$ , there does not exist an integer  $q > 1$  such that  $a^{2} \mid r$ .

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