
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 $\triangle ABC$ with interior angles $A$, $B$, and $C$, the sides opposite to these angles are $a$, $b$, and $c$, respectively. The area $S$ of $\triangle ABC$ is given by $S= \frac{\sqrt{3}}{2}\vec{AB}\cdot\vec{AC}$.
- (I) Determine the magnitude of angle $A$.
- (II) If $b+c=5$ and $a=\sqrt{7}$, find the area of $\triangle ABC$.

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