
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
Three math teachers and three language teachers are to be assigned to two different schools, with three teachers at each school, and each school must have both math and language teachers. How many different distribution plans are there?

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