
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 $- \frac{\pi}{2} < x < 0$, $\sin x + \cos x = \frac{1}{5}$, find the values of the following expressions:

$(1)$ The value of $\sin x - \cos x$

$(2)$ The value of $\frac{1}{{\cos }^{2}x - {\sin }^{2}x}$

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