
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 box has a total surface area of 150 square inches and the sum of the lengths of all its edges is 60 inches. Additionally, the volume of the box is 216 cubic inches. What is the sum of the lengths in inches of all of its interior diagonals?
A) $10\sqrt{3}$
B) $20\sqrt{2}$
C) $20\sqrt{3}$
D) $30\sqrt{3}$
E) $40\sqrt{2}$

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