
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 5 inches and a height of 7 inches. The radius of one cylinder is doubled and the height of the other is tripled. After these modifications, both dimensions (radius for the first and height for the second) are then increased by the same nonzero number of inches $x$. If the resulting volumes are equal, find the value of $x$. Express your answer as a common fraction.

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