
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 have heights and radii of the bases equal to $10 \mathrm{~cm} \times 10 \mathrm{~cm}$, $10 \mathrm{~cm} \times 5 \mathrm{~cm}$, and $20 \mathrm{~cm} \times 5 \mathrm{~cm}$, and volumes $V_{1}, V_{2}$, and $V_{3}$, 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 $V_{4}$ whose volume is between $V_{2}$ and $V_{3}$.

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

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