
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 $a$, $b$, and $c$ are the three internal angles of $\triangle ABC$, and $B$ and $C$ are the sides opposite to the angles $b$ and $c$ respectively. The equation $2b \cos A = a \cos C + c \cos A$ is known.

1. Find the measure of angle $A$.
2. If the perimeter of $\triangle ABC$ is 8, and the radius of the circumscribed circle is $\sqrt{3}$, find the area of $\triangle ABC$.

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