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

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