
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 $f(x)=\sqrt{3}\sin (2x+\frac{\pi }{6})+\cos (2x+\frac{\pi }{6})$.

(I) Find the interval where the function $f(x)$ is monotonically decreasing;

(II) In $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. If $f(A)=\sqrt{3}$, $\sin C=\frac{1}{3}$, $a=3$, find the value of $b$.

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