
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
Distribute 6 positions among 3 schools, with each school receiving at least one position and the number of positions allocated to each school being distinct, and calculate the number of possible distribution methods.

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