
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
Consider a cylindrical container with a radius $R = 10$ inches and a height $H = 5$ inches. The volume $V = \pi R^2 H$ is to be increased by the same fixed positive amount when $R$ is increased by $2x$ inches as when $H$ is increased by $3x$ inches. Determine the value of $x$ that satisfies this condition.
A) 0
B) 2
C) 5
D) 10
E) 15

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