
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) $$\frac{\sin^2{35^\circ} - \frac{1}{2}}{\cos{10^\circ} \cos{80^\circ}}$$
(2) $$\left(\frac{1}{\tan\frac{\alpha}{2}} - \tan\frac{\alpha}{2}\right) \cdot \frac{1 - \cos{2\alpha}}{\sin{2\alpha}}$$.

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