
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 acute triangle $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. Vector $\overset{⇀}{m}=(2\sin (A+C), \sqrt{3})$, vector $\overset{⇀}{n}=(\cos 2B,1-2{\cos }^{2} \frac{B}{2})$, and $\overset{⇀}{m}$ is parallel to $\overset{⇀}{n}$.

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

(2) If $\sin A\sin C=\sin ^{2}B$, find the value of $a-c$.

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