
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 set $A=\{n|n\in\mathbb{N}, 1\leq n\leq 500\}$. Define a function $f(n)=\log_{(n+1)}(n+2)$ on $A$. Then, the set $M=\{k|k=f(1)f(2)\ldots f(n), k\in\mathbb{N}\}$ can be represented by enumeration as.

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