
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 $sin(\pi -\alpha) - cos(\pi + \alpha) = \frac{\sqrt{2}}{3}$ $( \frac{\pi}{2} < \alpha < \pi )$.
Find: (1) $sin(\alpha) - cos(\alpha)$;  
(2) $sin^3(2\pi - \alpha) + cos^3(2\pi - \alpha)$.

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