
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
(1) Simplify: $\frac{\sin^{2} x}{\sin x - \cos x} - \frac{\sin x + \cos x}{\tan^{2} x - 1} - \sin x$;

(2) Given $\cos (\frac{\pi}{6} - \alpha) = \frac{\sqrt{3}}{3}$, find the value of $\cos (\frac{5}{6} \pi + \alpha) + \cos^{2} (\frac{4 \pi}{3} + \alpha)$.

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