
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 now has 4 chickens, 3 dogs, and 5 cats, along with 2 empty cages. In how many ways can these 14 entities be placed in a row of 14 cages, such that:
1. All animals of each type are in adjacent cages.
2. All groups of animals, except for one group, are separated by at least one empty cage.
3. The two animals of the same species are considered distinguishable.

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