
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
Consider the function  $ f(\theta) \equal{} \int_0^1 |\sqrt {1 \minus{} x^2} \minus{} \sin \theta|dx$  in the interval of  $ 0\leq \theta \leq \frac {\pi}{2}$ .

(1) Find the maximum and minimum values of  $ f(\theta)$ .

(2) Evaluate  $ \int_0^{\frac {\pi}{2}} f(\theta)\ d\theta$ .

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