
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
Three cylinders with volumes \(V_{1}, V_{2}\), and \(V_{3}\) have base heights and radii equal to 10 and 10 cm, 10 and 5 cm, and 20 and 5 cm, respectively.

(a) Write in ascending order the volumes \(V_{1}, V_{2}\), and \(V_{3}\) of the three cylinders.

(b) Give the dimensions of a cylinder with volume \(V_{4}\) that is between \(V_{2}\) and \(V_{3}\).

(c) Give the dimensions of a cylinder with volume \(V_{5}\) that is between \(V_{1}\) and \(V_{3}\).

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