
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 a cone and a cylinder made of rubber, the cone has a base radius of $5$ and a height of $4$, while the cylinder has a base radius of $2$ and a height of $8$. If they are remade into a new cone and a new cylinder with the same base radius, while keeping the total volume and height unchanged, find the new base radius.

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