
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 the function $f(x)=\sqrt{3}\cos^{2}x+\sin x\cos x$.
(I) Find the range of $f(x)$ when $x\in[0,\frac{\pi}{2}]$.
(II) In triangle $ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. If $f(\frac{A}{2})=\sqrt{3}$, $a=4$, and $b+c=5$, find the area of triangle $ABC$.

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