
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) Given $\pi < \alpha < 2\pi$, and $\cos\alpha= \frac{3}{5}$, find the value of $\cos(5\pi+\alpha) \cdot \tan(\alpha-7\pi)$;  
(2) Given $\cos\left( \frac{\pi}{6} - \alpha \right) = \frac{\sqrt{3}}{3}$, find the value of $\sin\left( \frac{\pi}{3} + \alpha \right)$.

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