
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
A pair of natural numbers \((a, p)\) is called good if the number \(a^3 + p^3\) is divisible by \(a^2 - p^2\), and \(a > p\).

(a) Indicate any possible value of \(a\) for which the pair \((a, 17)\) is good.

(b) Find the number of good pairs \((a, p)\) where \(p\) is a prime number less than 18.

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