
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 paper with radius $R$ is used to construct a cone by removing a sector and joining the edges to form the cone without overlap. The resulting cone has a radius of 15 cm and a volume of $675\pi$ cubic centimeters. Calculate the number of degrees in the measure of the angle of the sector that Jeff did not use for making the cone.

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