
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 $BC$, Mia removes the unshaded sector shown. Using the larger shaded sector, she joins edge $BC$ to edge $BA$ (without overlap) to form a cone of radius 8 centimeters and of volume $256\pi$ cubic centimeters.  What is the number of degrees in the measure of angle $ABC$ of the sector that is not used?

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