
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 opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. Given $c=2$, vectors $\overset{→}{m}=(c, \sqrt{3}b)$, $\overset{→}{n}=(\cos C,\sin B)$, and $\overset{→}{m}$ is parallel to $\overset{→}{n}$.

(1) Find the measure of angle $C$;
(2) If $\sin (A+B)$, $\sin 2A$, $\sin (B-A)$ form an arithmetic sequence, find the length of side $a$.

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