
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 $f(x) = \begin{cases} x+1 & ,(-1 \leq x \leq 0) \\ \sqrt{1-x^2} & ,(0 < x \leq 1) \end{cases}$, find the value of $\int_{-1}^{1} f(x) \, dx$.

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