
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 high school has three math teachers. To facilitate students, math teachers are scheduled for duty from Monday to Friday, with two teachers on duty on Monday. If each teacher is on duty for two days a week, then there are ________ possible duty arrangements for the week.

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