
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 circular piece of cardboard has a radius of 18 cm, from which a sector is removed as shown in the glossary. This larger shaded sector is then used to form a cone by bringing edge BC to edge BA. The resulting cone has a radius of 15 centimeters and a volume of $1350\pi$ cubic centimeters. Determine the degrees in the measure of angle ABC, representing the sector that Jeff did not use.

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