
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]


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Two congruent cylinders each have a radius of 5 inches and a height of 4 inches. The radius of one cylinder is increased by 2 inches, and the height of the other cylinder is increased by a different non-zero number of inches, denoted as \( y \). If the resulting volumes of both cylinders are equal, how many inches is the increase \( y \)?

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