
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 angles of elevation of the top of a pole from points A, B, and C on the ground are α, β, and γ respectively. The points are 10 meters, 20 meters, and 30 meters away from the bottom of the pole, and the sum of the angles is 90°. What is the height of the pole in meters?

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