
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 $-\frac{\pi}{2} < x < 0$, and $\sin x + \cos x = \frac{1}{5}$.
(I) Find the value of $\sin x - \cos x$;
(II) Find the value of $\frac{3 \sin^2 \frac{x}{2} - 2 \sin \frac{x}{2} \cos \frac{x}{2} + \cos \frac{2x}{2}}{\tan x + \frac{1}{\tan x}}$.

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