
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, ensuring that each school receives at least one position and that the number of positions each school receives is distinct, and calculate the total number of possible distributions.

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