
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
Consider a \(p\)-pointed star where \(p\) is a positive integer such that \(p\) is the product of two distinct prime numbers \(a\) and \(b\), (\(p = ab\)), and \(a < b\). Assume the same conditions for regularity and symmetry as in the original problem of the \(n\)-pointed star. How many non-similar regular \(p\)-pointed stars are there?

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