
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
 $p$  is a prime number such that its remainder divided by 8 is 3. Find all pairs of rational numbers  $(x,y)$  that satisfy the following equation.  $$ p^2 x^4-6px^2+1=y^2 $$  

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