
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 sequences $\left\{a_{1}, a_{2}, \cdots\right\}$ such that:
$a_{1}=1$ and $\left|a_{n}-a_{m}\right| \leq \frac{2mn}{m^{2}+n^{2}}$ (for all positive integers $m, n$).

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