
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
The three-sided roof of a tower in King Arthur's castle is topped with a triangular pyramid where all plane angles at the vertex are right angles. The three slopes of the roof are painted in different colors. The red slope is inclined to the horizontal at an angle $\alpha$, and the blue slope at an angle $\beta$. Find the probability that a raindrop, vertically falling on a random spot on the roof, lands on the green slope.

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