
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
Simplify:
$(1)\ \sin 420^{\circ}\cos 330^{\circ}+\sin (-690^{\circ})\cdot\cos (-660^{\circ})$;
$(2)\ \frac {\sin ( \frac {\pi}{2}+\alpha)\cos ( \frac {\pi}{2}-\alpha)}{\cos (\pi+\alpha)}+ \frac {\sin (\pi-\alpha)\cos ( \frac {\pi}{2}+\alpha)}{\sin (\pi+\alpha)}$.

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