
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
Given that 4 plumbers are to be distributed to 3 different residents' houses for heating pipe inspection, where all plumbers must be allocated and each resident's house must be inspected, determine the total number of possible allocation schemes.

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