
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
Given that there are  $24$  primes between  $3$  and  $100$ , inclusive, what is the number of ordered pairs  $(p, a)$  with  $p$  prime,  $3 \le p < 100$ , and  $1 \le a < p$  such that  $p \mid (a^{p-2} - a)$ ?

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