
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 a circular piece of paper with radius \( DE \), Sarah removes the unshaded sector shown. Using the larger shaded sector, she joins edge \( DE \) to edge \( DA \) (without overlap) to form a cone of radius 15 centimeters and of volume \( 675\pi \) cubic centimeters. What is the number of degrees in the measure of angle \( EDA \) of the sector that is not used?

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