
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 certain high school plans to offer three elective math courses for the second year of high school next semester: "Matrix and Transformation", "Information Security and Cryptography", and "Switch Circuits and Boolean Algebra". Among the 10 math teachers planned to teach the second year of high school, 3 can only teach "Matrix and Transformation", 2 can only teach "Information Security and Cryptography", and another 3 can only teach "Switch Circuits and Boolean Algebra". Only 2 teachers can teach all three courses. Now, 9 out of these 10 teachers need to be selected to teach these three elective courses, with each course being taught by 3 teachers. The total number of different arrangements is.

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