
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 that $\triangle ABC$ is inscribed within a unit circle, with $\angle A$ being an acute angle, and $a$, $b$, $c$ representing the lengths of the sides opposite to $A$, $B$, $C$ respectively. Also, $2acosA=ccosB+bcosC$.

(I) Find the value of $cosA$;

(II) If $b^2+c^2=4$, find the area of $\triangle ABC$.

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