
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
Calculate the values of the following trigonometric functions:
(1) $\sin \frac {4\pi}{3} \cdot \cos \frac {25\pi}{6} \cdot \tan \frac {5\pi}{4}$;
(2) $\sin \left[(2n+1)\pi - \frac {2\pi}{3}\right]$.

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