
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 tank has a radius \( R = 5 \) inches and a height \( H = 6 \) inches. Calculate the value of \( x \) such that increasing the radius by \( x \) inches results in the same volume increase as increasing the height by \( 2x \) inches.

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