
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
Observation:
$(1)\tan 10^{\circ}\tan 20^{\circ}+\tan 20^{\circ}\tan 60^{\circ}+\tan 60^{\circ}\tan 10^{\circ}=1$;
$(2)\tan 5^{\circ}\tan 10^{\circ}+\tan 10^{\circ}\tan 75^{\circ}+\tan 75^{\circ}\tan 5^{\circ}=1$.
Based on the above two equations, generalize and write your conclusion.

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