
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 are 64 small wooden cubes with an edge length of 1. Each cube has two faces painted red, and the other faces are white. Among these cubes, 20 have two adjacent faces painted red, and 44 have two opposite faces painted red. If these cubes are assembled to form one large cube, what is the maximum possible area of the red surface on the large cube?

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