
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 a function $f(x)$ on $\mathbb{R}$ that satisfies $f(x+6)=f(x)$. When $-3\leqslant x\leqslant -1$, $f(x)=-{(x+2)}^{2}$; when $-1 < x < 3$, $f(x)=x$. Then, calculate the value of $f(1)+f(2)+f(3)+\cdots+f(2013)$.

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