
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
(1) Simplify: $\dfrac{\cos 2\alpha }{2\tan (\dfrac{\pi }{4}-\alpha ){{\sin }^{2}}(\dfrac{\pi }{4}+\alpha )}$;

(2) Evaluate: $\tan {{70}^{\circ }}\cos {{10}^{\circ }}(\sqrt{3}\tan {{20}^{\circ }}-1)$;

(3) Evaluate: $\cos {{20}^{\circ }}\cos {{40}^{\circ }}\cos {{60}^{\circ }}\cos {{80}^{\circ }}$.

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