
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
 $\boxed{N1}$ Let  $n$  be a positive integer, $g(n)$  be the number of positive divisors of  $n$  of the form  $6k+1$  and  $h(n)$  be the number of positive divisors of  $n$  of the form  $6k-1,$ where  $k$  is a nonnegative integer.Find all positive integers  $n$  such that  $g(n)$  and  $h(n)$  have different parity.

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