
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) Provide any possible value of $a$ for which the pair $(a, 19)$ is good.

(b) Find the number of good pairs for which $p$ is a prime number less than 24.

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