
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
From point $C$, at a distance of $100 \mathrm{~m}$, we observe the cross at the top of tower $A B$ at an angle $\alpha$, and from a distance of $250 \mathrm{~m}$, we observe it at an angle of $\frac{\alpha}{2}$. How tall is the tower?

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