
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 Happy Valley Kennel expands, now hosting 3 chickens, 3 dogs, and 6 cats, and also has a setting of 15 cages. Among these 15 cages, three must always remain empty. In how many ways can the 12 animals be placed in the 12 cages, such that all of the animals of each type are in adjacent cages, keeping 3 specified cages empty?

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