
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 cylinder has a radius of $6$ cm and a height assumed to be equal to its radius. A straight cut through the cylinder (centered and perpendicular to its base) divides it into two equal halves. What is the volume of one half of this cylinder?
A) 339 cm³
B) 378 cm³
C) 419 cm³
D) 450 cm³
E) 603 cm³

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