
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 the equality \(\left(a^{m_{1}}-1\right) \ldots \left(a^{m_{n}}-1\right) = \left(a^{k_{1}}+1\right) \ldots \left(a^{k_{l}}+1\right)\), where \(a, n, l,\) and all exponents are natural numbers, with \(a > 1\).

Find all possible values of \(a\).

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