
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
Four students and two teachers are taking a commemorative photo together. How many different seating arrangements are there for each of the following cases? (Please provide numerical answers)
(1) The teachers must sit in the middle;
(2) The teachers cannot sit at the ends, but must sit together;
(3) The teachers cannot sit at the ends, nor can they sit adjacent to each other.

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