
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 $f(x) = 2\sqrt{3}\sin\frac{x}{2}\cos\frac{x}{2} + 2\cos^2\frac{x}{2}$.

(I) Find the smallest positive period of $f(x)$ and the interval where it is monotonically decreasing;

(II) If $f(B) = 3$, in $\triangle ABC$, where the sides opposite angles A, B, and C are denoted as $a$, $b$, and $c$ respectively, and given $b = 3$, $\sin C = 2\sin A$, find the values of $a$ and $c$.

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