
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
For positive integers $N$, define $N$ to be $5$-nice if there exists a positive integer $a$ such that $a^{5}$ has exactly $N$ positive divisors. Define $N$ as $6$-nice under similar terms for $a^6$. Find the number of positive integers less than $500$ that are neither $5$-nice nor $6$-nice.

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