
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
Let $f(x) = \begin{cases} \sqrt{1-x^2}, & x\in[-1,1) \\ x^2-1, & x\in[1,2] \end{cases}$. Find the value of $\int_{-1}^{2}f(x)dx$.

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