
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 there are 15 dogs including Rex and Daisy. We need to divide them into three groups of sizes 6, 5, and 4. How many ways can we form the groups such that Rex is in the 6-dog group and Daisy is in the 4-dog group?

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