
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 Youth Park in Shenhe District, Shenyang City, within the winding South Canal strip park, covering an area of 8000 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 elevation angle of the top of the tower (point B) from point A in Youth Park to be 45°. On the horizontal ground, walking 129 meters along the straight line connecting point A and the center of the tower base (point C) to reach point D (assuming it can be reached), the elevation angle of the top of the tower (point B) at this point is 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 (accurate to 1 meter).

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