
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
(I) Find the value of $\sin (-\frac{10\pi}{3})$;
(II) Simplify: $\frac{\sin (\pi+\alpha)\cos (\alpha-\pi)\tan (3\pi-\alpha)}{\sin (\frac{\pi}{2}-\alpha)\cos (\frac{5\pi}{2}+\alpha)\tan (\alpha-9\pi)}$.

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