
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
In a school club of twelve students, each student is to team up with exactly three other students for various activities. We define two teaming arrangements as different if and only if there is at least one student who teams up with different students under the two arrangements. How many different ways can the teaming arrangements be created, and what is the remainder when this total is divided by 1000?

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