
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 angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. Given vectors $\vec{m}=(2\sin \frac{A}{2}, \sqrt{3})$ and $\vec{n}=(\cos A, 2\cos^{2} \frac{A}{4} - 1)$, and $\vec{m}$ is parallel to $\vec{n}$.
(I) Find the measure of angle $A$;
(II) If $a= \sqrt{7}$ and the area of triangle $ABC$ is $\frac{3\sqrt{3}}{2}$, find the value of $b+c$.

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