
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 wooden rectangular prism with dimensions 4 by 5 by 6 is painted green and then cut into 1 by 1 by 1 cubes. Determine the ratio of the number of cubes with exactly two green faces to the number of cubes with three green faces.

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