
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
A school selects 5 teachers, namely A, B, C, D, and E, to support teaching in three remote schools, with at least 1 person in each school. A and B must go to the same school, and A and C cannot go to the same school. The total number of different dispatch plans is $\boxed{\text{number}}$.

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