
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
Let \( n \) be an integer of the form \( a^2 + b^2 \), where \( a \) and \( b \) are relatively prime integers. If \( p \) is a prime number such that \( p \leq \sqrt{n} \), then \( p \) divides \( ab \). Determine all such \( n \).

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