
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
There are two pieces of wood, one rectangular and one cylindrical, with the same height and a volume ratio of 1:1. If the rectangular wood is processed into the largest possible cylinder and the cylindrical wood is processed into the largest possible rectangular prism, what is the ratio of the volume of the cylinder to the volume of the rectangular prism? $\qquad$.

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