
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 $\sin (x- \frac{\pi}{4})= \frac{7 \sqrt{2}}{10}$ and $\cos 2x= \frac{7}{25}$, find the value of $\cos (\frac{7\pi}{12}-x)$ and evaluate $\frac{\sin 2x+2\sin ^{2}x}{1-\tan x}$.

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