
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 radius \( R \) of a conical tent is \( 5 \) meters and the height \( H \) is \( 12 \) meters. The volume \( V \) of a cone is increased by the same fixed amount when \( R \) is increased by \( y \) meters as when \( H \) is increased by \( y \) meters. Determine the possible real value of \( y \) that satisfies this condition.
A) \(\frac{31}{12}\) meters
B) \(-10.5\) meters
C) \(12\) meters
D) No such value exists

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