
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
(The full score for this question is 12 points)

In $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are respectively $a$, $b$, $c$, and it satisfies $\cos A = \frac{b^2 + c^2 - a^2}{2bc} = \frac{1}{2}$, and $bc = 3$.

(1) Find the area of $\triangle ABC$;

(2) If $c = 1$, find the value of $a$.

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