
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 that $\cos \left( x- \frac{\pi }{4} \right)=\frac{\sqrt{2}}{10}$, and $x\in \left( \frac{\pi }{2},\frac{3\pi }{4} \right)$.

(1) Find the value of $\sin x$;

(2) Find the value of $\sin \left( 2x+\frac{\pi }{3} \right)$.

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