
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 sports team in a certain class consists of 18 soccer players, 12 basketball players, and 6 table tennis players (each person participates in only one sport). Now, a sample of size $n$ is drawn from these athletes. If both systematic sampling and stratified sampling methods are used, no individuals need to be excluded; when the sample size is $n+1$, if systematic sampling is used, 1 individual needs to be excluded. Then, the sample size $n$ is \_\_\_\_\_.

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