
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
Two congruent cylinders each have a radius of 6 inches and a height of 4 inches. Both cylinders' heights are increased by 2 inches, and the radius of one cylinder is increased by an unknown number x of inches such that their volumes remain equal. What is the value of x? Express your answer as a common fraction.

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