
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]


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In a mathematics conference, there are five teachers from three schools, \\(A\\), \\(B\\), and \\(C\\), with \\(A\\) having 2 teachers, \\(B\\) having 2 teachers, and \\(C\\) having 1 teacher. Now, the five teachers are to line up for a photo. If teachers from the same school must not stand next to each other, there are \_\_\_\_\_\_ different ways for them to line up.

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