
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
At points A, B, and C, which are respectively 80m, 160m, and 240m horizontally away from the base of a tower, the angles of elevation to the top of the tower are measured to be $α$, $β$, and $γ$. If $α+β+γ=90°$, then the height of the tower is ________.

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