
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
Find the sum of all integers  $m$  with  $1 \le m \le 300$  such that for any integer  $n$  with  $n \ge 2$ , if  $2013m$  divides  $n^n-1$  then  $2013m$  also divides  $n-1$ .

*Proposed by Evan Chen*

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