
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
There is a cube $A B C D-E F G H$, with three square faces passing through point $B$ painted red. The cube is then cut along several of its edges to form a net. If none of the three red squares share a common edge in the net, how many different ways are there to make the cuts? (Two ways are considered the same if they involve the same edges, regardless of the order in which they are cut).

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