
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
Let  $n$  be a natural number. An integer  $a>2$  is called  $n$ -decomposable, if  $a^n-2^n$  is divisible by all the numbers of the form  $a^d+2^d$ , where  $d\neq n$  is a natural divisor of  $n$ . Find all composite  $n\in \mathbb{N}$ , for which there's an  $n$ -decomposable number.

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