
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
Given the function $f(x)= \begin{cases}x^{2} \\\\ x+1\\end{cases} \quad \begin{matrix}-2\leqslant x\leqslant 0 \\\\ 0 < x\leqslant 2\\end{matrix}$, find the value of $\int_{-2}^{2}f(x)dx$.

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