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

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