
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 all strictly positive integers \(a, m, n\) such that

\[
(a+1)\left(a^{2}+a+1\right) \cdots\left(a^{n}+a^{n-1}+\cdots+1\right) = a^{m}+a^{m-1}+\cdots+1
\]

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