
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
Consider the following trigonometric identities:  
① $\tan(10^\circ)\tan(20^\circ) + \tan(20^\circ)\tan(60^\circ) + \tan(60^\circ)\tan(10^\circ) = 1$;  
② $\tan(13^\circ)\tan(35^\circ) + \tan(35^\circ)\tan(42^\circ) + \tan(42^\circ)\tan(13^\circ) = 1$;  
③ $\tan(5^\circ)\tan(100^\circ) + \tan(100^\circ)\tan(-15^\circ) + \tan(-15^\circ)\tan(5^\circ) = 1$  
④ $\tan(-160^\circ)\tan(-22^\circ) + \tan(-22^\circ)\tan(272^\circ) + \tan(272^\circ)\tan(-160^\circ) = 1$  
In general, if $\tan\alpha$, $\tan\beta$, and $\tan\gamma$ all exist, please conjecture a conclusion that you can draw from these four identities.

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