
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 cylinder has a radius of 10 inches and a height of 5 inches. Both the radius and the height of this cylinder are increased by the same nonzero number of inches. The volume of the new cylinder is found to be four times the volume of the original cylinder. What is the increase in inches?

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