
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 vectors $\overrightarrow{m}=(2\sin x,1)$, $\overrightarrow{n}=(\sqrt{3}\cos x,2\cos^2 x)$, define the function $f(x)= \overrightarrow{m}\cdot \overrightarrow{n}$.
(Ⅰ) Find the range of the function $f(x)= \overrightarrow{m}\cdot \overrightarrow{n}$ when $x\in \left[0, \frac{\pi}{2}\right]$.
(II) In triangle $ABC$, let $a$, $b$, and $c$ be the sides opposite to angles $A$, $B$, and $C$ respectively, with $a=l$, $b=\sqrt{3}$, and $f(A)=3$. Determine the measure of angle $C$.

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