
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
In triangle $ABC$, the sides opposite to the internal angles $A$, $B$, $C$ are $a$, $b$, $c$, respectively. It is known that $2\cos A(c\cos B + b\cos C) = a$.
$(I)$ Find the measure of angle $A$;
$(II)$ If the area of triangle $ABC$ is $\frac{\sqrt{3}}{4}$, and $c^2 + ab\cos C + a^2 = 4$, find the value of $a$.

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