
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
A factory implements a coal-to-electricity project to prevent and control smog and plans to dismantle a chimney with height AB. Surveyors select two observation points C and D on the same horizontal plane as the bottom of the chimney B, measuring $\angle BCD=75^\circ$, $\angle BDC=60^\circ$, and CD=40 meters. At point C, directly above at point E, the elevation angle to the top A is $30^\circ$, and CE=1 meter. Find the height of the chimney AB in meters.

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