
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 Leifeng Pagoda on Xizhao Mountain in Hangzhou is one of the Ten Scenes of Hangzhou. To measure the height of the Leifeng Pagoda (BC), the distance from the foot of the mountain (A) is measured to be AC = 62√2m. The angle of elevation to the top of the tower (B) is α = 45°, and the slope angle of the mountain is known to be β = 15°. Calculate the height of the Leifeng Pagoda (BC).

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