
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
Consider the same cube as described. If a path from $A$ to $B$ must now be exactly 4 edges long, allowing for backtracking (i.e., moving along an edge already traversed in the previous step), how many different 4-edge paths are there from $A$ to $B$?

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