
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
The height of a cylinder is equal to the radius of its base and has a length of \( r \).

a. A cylindrical surface is drawn through the axis of the cylinder, dividing the circumference of the base into two arcs with lengths in the ratio of 2:1. This cylindrical surface divides the given cylinder into two parts. Find the lateral surface area and the volume of the larger part of the cylinder.

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