
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)\equal{}\frac{1}{\sin x\sqrt{1\minus{}\cos x}}\ (0<x<\pi)$ .

(1) Find the local minimum value of  $ f(x)$ .

(2) Evaluate  $ \int_{\frac{\pi}{2}}^{\frac{2\pi}{3}} f(x)\ dx$ .

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