
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 \( N \) and \( k \), define \( N \) to be \( k \)-nice if there exists a positive integer \( a \) such that \( a^{k} \) has exactly \( N \) positive divisors. Find the number of positive integers less than \( 500 \) which are neither \( 3 \)-nice nor \( 5 \)-nice.

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