
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 12 rabbit holes. Holes numbered 1 through 9 together have a total of 32 rabbits. Holes numbered 4 through 12 together have a total of 28 rabbits. Holes numbered 1 through 3 and 7 through 12 together have a total of 34 rabbits. Holes numbered 1 through 6 and 10 through 12 together have a total of 29 rabbits. How many different possible distributions of rabbits are there in each of the holes?

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