
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
Find the values of the following expressions:
(1) $\sec 50^{\circ}+\tan 10^{\circ}$;
(2) $\cos \frac{2 \pi}{7}+\cos \frac{4 \pi}{7}+\cos \frac{6 \pi}{7}$;
(3) $\tan 6^{\circ} \tan 42^{\circ} \tan 66^{\circ} \tan 78^{\circ}$.

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