
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 $\cos x - \sin x = \frac{3\sqrt{2}}{5}$ and $\frac{5\pi}{4} < x < \frac{7\pi}{4}$,

1. Find the value of $\sin x + \cos x$;
2. Find the value of $\frac{\sin 2x - 2\sin^2 x}{1 + \tan x}$.

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