
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 water tank has a radius $R$ of $10$ inches and a height $H$ of $5$ inches. Determine the value of $x$ such that the increase in volume, when the radius is increased by $x$ inches, is twice the increase in volume when the height is increased by $x$ inches.
A) $x = 0$  
B) $x = 10$  
C) $x = 20$  
D) $x = 40$

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