
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 hotel arranges for five people, labeled \\(A\\), \\(B\\), \\(C\\), \\(D\\), and \\(E\\), to stay in three rooms, with each room housing at least one person. Given that \\(A\\) and \\(B\\) cannot stay in the same room, there are \_\_\_\_\_\_ different arrangements possible (Answer with a number).

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