
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
Given a circular iron plate with a radius of 1 decimeter, find the value of the central angle $x$ in radians for which the volume of the cone formed by rolling the remaining part of the plate after cutting out the sector reaches its maximum.

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