
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 has a sum of squares of its side lengths ($x^2 + y^2 + z^2$) equal to 50 and the sum of the products of its dimensions taken two at a time ($xy + yz + zx$) equal to 47. What is the sum of the lengths of all its interior diagonals?
A) $8\sqrt{3}$
B) $20$
C) $16\sqrt{3}$
D) $20\sqrt{2}$
E) $40\sqrt{2}$

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