
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 $\{a_{1}, a_{2}, \cdots\}$ that satisfy the following conditions:
\[ a_{1} = 1 \]
and
\[ \left|a_{n} - a_{m}\right| \leq \frac{2mn}{m^{2} + n^{2}} \]
for all positive integers $m$ and $n$.

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