
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 A due east of a certain TV tower, the angle of elevation to the top of the tower is measured to be $60^{\circ}$; from point B southwest of the tower at an angle of $30^{\circ}$, the angle of elevation to the top of the tower is measured to be $45^{\circ}$. The distance between A and B is $35 m$. Determine the height of this TV tower.

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