
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 cylindrical can has a radius \( R = 5 \) inches and a height \( H = 4 \) inches. If you increase both the radius and the height each by \( y \) inches, it results in the same volume increase as when only the radius is increased by \( 2y \) inches. Find the value of \( y \).
A) \( y = \sqrt{76} - 5 \) \\
B) \( y = 5 - \sqrt{76} \) \\
C) \( y = \sqrt{51} \) \\
D) \( y = \sqrt{76} \)

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