
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 the following expressions:

(1) $\dfrac{\sin^{2} 35^{\circ} - \frac{1}{2}}{\cos 10^{\circ} \cos 80^{\circ}}$

(2) $\left(\dfrac{1}{\tan \frac{\alpha}{2}} - \tan \frac{\alpha}{2}\right) \cdot \dfrac{1 - \cos 2\alpha}{\sin 2\alpha}$

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