
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
The familiar  $3$ -dimensional cube has  $6$   $2$ -dimensional faces,  $12$   $1$ -dimensional edges, and  $8$   $0$ -dimensional vertices. Find the number of  $9$ -dimensional sub-subfaces in a  $12$ -dimensional cube.

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