
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 $$f(x)= \begin{cases} \left.\begin{matrix}x^{2} \\ x+1\end{matrix}\right.\end{cases}$$ $$\left.\begin{matrix}-2≤x≤0 \\ 0＜x≤2\end{matrix}\right.$$ calculate the value of $$∫ \left.\begin{matrix}2 \\ -2\end{matrix}\right.f(x)dx$$.

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