
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
In triangle $ABC$, given that $A + B + C = \pi$, we have $A + B = \pi - C$, then $\tan(A + B) = \tan(\pi - C)$. Simplifying this expression, we get $\tan A + \tan B + \tan C = \tan A \tan B \tan C$. Using an analogy with this method, if the acute angles $\alpha$, $\beta$, and $\gamma$ satisfy $\alpha + \beta + \gamma = \frac{\pi}{2}$, then the conclusion that $\tan \alpha$, $\tan \beta$, and $\tan \gamma$ satisfy is \_\_\_\_\_\_.

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