
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
Consider infinite sequences  $a_1,a_2,\dots$  of positive integers satisfying  $a_1=1$  and   $$ a_n \mid a_k+a_{k+1}+\dots+a_{k+n-1} $$   for all positive integers  $k$  and  $n.$  For a given positive integer  $m,$  find the maximum possible value of  $a_{2m}.$ *Proposed by Krit Boonsiriseth*

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