
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
Five outstanding teachers from Yuyin School are sent to three middle schools in remote areas for teaching exchange, with at least one teacher assigned to each school. Determine the total number of different allocation methods.

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