
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 value of the following expressions:

(1) $\cos (- \frac{11\pi}{6}) + \sin \frac{12\pi}{5} \cdot \tan 6\pi$;

(2) $\sin 420^{\circ}\cos 750^{\circ} + \sin (-330^{\circ})\cos (-660^{\circ})$.

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