
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 rectangular prism with integer edge lengths has all 6 of its faces painted red. It is then cut into small cubes with edge lengths of 1 cm. Among these small cubes, there are 24 cubes with exactly one red face and 28 cubes with exactly two red faces. What is the original volume of the rectangular prism in cubic centimeters?

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