
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
We construct a cube frame using wire segments with a resistance of $1 \Omega$, meaning a cube that only has its edges. An electric current of $i$ flows through the cube. What will be the currents along each edge, and what will be the equivalent resistance of our cube frame, if we replace it with a single conductor, in the cases where a) an electric potential is applied across one of the body diagonals, and b) an electric potential is applied across one of the face diagonals?

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