
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 $\sin \left( \frac{\pi}{4}-x\right)= \frac{1}{5} $, and $-\pi < x < - \frac{\pi}{2}$. Find the values of the following expressions:

$(1)\sin \left( \frac{5\pi}{4}-x\right)$;  

$(2)\cos \left( \frac{3\pi}{4}+x\right)$; 

$(3)\sin \left( \frac{\pi}{4}+x\right)$．

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