
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
Given an infinite sequence $\left\{a_{n}\right\}$ satisfies: $a_{n}$ is a positive integer, $a_{1}=1$, and for any positive integers $k$ and $n$,
$$
a_{n} \mid\left(a_{k}+a_{k+1}+\cdots+a_{k+n-1}\right) \text {. }
$$

Given a positive integer $m$, find the maximum value of $a_{2 m}$.

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