
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
Given the volume of a cylinder is given by the formula $V=\pi r^2h$, increasing the radius by $3$ units and the height by $3$ units increased the volume by $z$ cubic units. If increasing either the radius by $3$ units or the height by $3$ units increases the volume by the same amount, $z$, find the original radius if the original height is $3$.

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