
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 Liaoning Broadcasting and Television Tower is located on the west side of the Youth Park in Shenhe District, Shenyang City, within the winding Nan Yun River strip park, covering an area of 8,000 square meters. The tower is divided into four parts: the base, the body, the tower building, and the mast. A math activity group measured the angle of elevation to the top of the tower (point B) from point A in the Youth Park to be 45°. On the ground, walking 129 meters along the straight line connecting point A and the center of the tower base (point C) to point D (assuming it can be reached), the angle of elevation to the top of the tower (point B) was measured to be 60°.  
(1) Based on the problem description, draw a simple relationship diagram among points A, B, C, and D;  
(2) Calculate the height of the Liaoning Broadcasting and Television Tower based on the measurement results (rounded to the nearest meter).

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