
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
In $\triangle ABC$, the sides $a$, $b$, and $c$ correspond to angles $A$, $B$, and $C$ respectively. Given $2\cos 2B=4\cos B-3$,

(I) Find the measure of angle $B$;

(II) If $S_{\triangle ABC}=\sqrt{3}$, and $a\sin A+c\sin C=5\sin B$, find side $b$.

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