
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 $f(x)=m\sin x+\cos x(x\in R)$ whose graph passes through the point $(\frac{\pi}{2},1)$.
(I) Find the analytical expression of $y=f(x)$, and determine the function's smallest positive period and extreme values.
(II) If $f(\frac{\pi}{12})=\sqrt{2}\sin A$, where $A$ is an internal angle of the acute triangle $\triangle ABC$ with an area of $\frac{3\sqrt{3}}{2}$ and $AB=2$, find the lengths of $AC$ and $BC$.

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