
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 college has 18 senior teachers, 12 first-level teachers, and 6 top-level teachers. A sample of size $n$ needs to be drawn from them to serve as representatives. If both systematic sampling and stratified sampling methods are used for drawing the sample, no individuals need to be excluded; if the sample size is increased by one, then when using systematic sampling, 1 person needs to be excluded from the total population. The sample size $n$ is ____.

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