
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
Define the function $f(x)$ on $\mathbb{R}$ such that $f(m+n^2) = f(m) + 2[f(n)]^2$, where $m, n \in \mathbb{R}$, and $f(1) \neq 0$. Find the value of $f(2013)$.

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