
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 a sequence of positive integers \(\left\{a_{n}\right\}\) that satisfies the conditions \(a_{m^{2}} = a_{m}^{2}\) and \(a_{m^{2} + k^{2}} = a_{m} a_{k}\) for any positive integers \(m\) and \(k\), find the general term of the sequence \(\left\{a_{n}\right\}\).

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