
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
Suppose we want to divide 12 dogs into three groups, one with 4 dogs, one with 6 dogs, and one with 2 dogs. How many ways can we form the groups such that Fluffy is in the 4-dog group and Nipper is in the 6-dog group?

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