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

A) $\frac{\pi}{2}+\frac{4}{3}$
B) $\frac{\pi}{2}+3$
C) $\frac{\pi}{4}+\frac{4}{3}$
D) $\frac{\pi}{4}+3$

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