
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 $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively, and it is given that $b\sin 2C=c\sin B$.

$(1)$ Find the size of angle $C$;

$(2)$ If $\sin \left( B- \frac{\pi}{3} \right)=\frac{3}{5}$, find the value of $\sin A$.

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