
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 $R = 10$ inches and height $H = 5$ inches. The volume of the tank is increased by the same fixed amount when the radius $R$ is multiplied by a factor $k$ as when the height $H$ is increased by $k$ inches. Determine the value of $k$ that satisfies this condition.

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