
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 $ABC$, it is given that $A + B + C = \pi$. Hence, $A + B = \pi - C$, which yields $\tan(A+B) = \tan(\pi-C)$. This simplifies to $\tan A + \tan B + \tan C = \tan A \cdot \tan B \cdot \tan C$. By analogy, if positive angles $\alpha$, $\beta$, and $\gamma$ satisfy $\alpha + \beta + \gamma = \frac{\pi}{2}$, then the conclusion satisfied by $\tan \alpha$, $\tan \beta$, and $\tan \gamma$ is _________.

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