
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
On a horizontal plane, three points are 100 meters, 200 meters, and 300 meters away from the base point of an antenna. The sum of the angles of elevation to the antenna from these three points is $90^{\circ}$. What is the height of the antenna?

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