
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 $x \in [-3,3)$, $f(x)=\begin{cases} -(x+2)^2, & -3 \leqslant x < -1 \\ x, & -1 \leqslant x < 3 \end{cases}$. Find $f(4)$ and the value of $f(1)+f(2)+f(3)+\ldots+f(2016)+f(2017)$.

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