
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
Six students, consisting of three boys and three girls, are to be distributed to three schools: Yucai, Yuren, and Yuhong. Yucai School will only accept one boy, and each of the other two schools must accept at least one student. Calculate the total number of possible distribution plans.

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