
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
Given 16 people consisting of 4 teachers from the first, second, and third grades of high school, as well as 4 other administrative staff, calculate the number of different selection methods to choose 3 leaders such that they cannot all be from the same department and at least 1 person is from the administrative department.

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