
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  $ p,\ q\ (p < q)$  be the  $ x$  coordinates of curves  $ x^2 \plus{} y^2 \equal{} 1,\ y\geq 0$  and  $ y \equal{} \frac {1}{4x}.$ 

(1)  Find  $ \alpha ,\ \beta$  such that  $ \cos \frac {\alpha}{2} \equal{} p,\ \cos \frac {\beta }{2} \equal{} q\ (0 < \alpha < \pi ,\ 0 < \beta < \pi).$ 

(2) Find the area bounded by the curves.

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