
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
(1) Given that $\cos \left( x-\dfrac{\pi }{4} \right)=\dfrac{\sqrt{2}}{10}, x \in \left( \dfrac{\pi }{2},\dfrac{3\pi }{4} \right)$, compute the value of $\sin x$;

(2) If $A,B$ are acute angles, and $\sin A=\dfrac{\sqrt{5}}{5}, \sin B=\dfrac{\sqrt{10}}{10}$, compute the value of $A+B$.

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