
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
An ordered pair  $(n,p)$  is *juicy* if  $n^{2} \equiv 1 \pmod{p^{2}}$  and  $n \equiv -1 \pmod{p}$  for positive integer  $n$  and odd prime  $p$ . How many juicy pairs exist such that  $n,p \leq 200$ ?


Proposed by Harry Chen (Extile)

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