
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 parallelepiped is cast from a piece of metal with mass $M$. Then, a source of constant voltage is connected to different pairs of mutually opposite faces of the parallelepiped. It turned out that the ratio of the thermal power released in the parallelepiped when the source is connected to different pairs of faces is 1:2:8. Find the edge lengths of the parallelepiped. The density of the metal $\rho$ is known. The connection of the parallelepiped to the source is carried out using wide buses that ensure the contact of the source with the entire area of the face, allowing the current spreading effects to be neglected.

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