
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 unit has 6 engineers, 12 technicians, and 18 craftsmen. A sample of capacity $n$ will be taken from these people. If systematic sampling and stratified sampling methods are used for extraction, no individual needs to be removed. However, if the sample capacity is increased by 1, one individual must be removed from the total population when using systematic sampling. Find the value of $n$.

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