
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 triplets  $(a,b,p)$  where  $a,b$  are positive integers and  $p$  is a prime number satisfying:  $\frac{1}{p}=\frac{1}{a^2}+\frac{1}{b^2}$ 

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