
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 highway design institute has 6 engineers, 12 technicians, and 18 workers. A total of $n$ individuals are to be selected from these people to attend a city-wide science and technology conference. If systematic sampling and stratified sampling methods are used to draw the participants without individual exclusion, but when using systematic sampling, if the number of participants increases by 1, 1 individual needs to be excluded from the total initially. Find the value of $n$.

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