
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
Three faces of a right rectangular prism have areas of 56, 63, and 72 square units. Find the volume of the prism, given that one of its dimensions is twice the size of another. Express your answer to the nearest whole number.

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