
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
Let \( S \) be a set of \( 7 \) integers taken from \( \{1, 2, \dots, 15\} \) with the property that if \( a \) and \( b \) are elements of \( S \) with \( a < b \), then \( b \) is not a multiple of \( a \). Find the median value of an element in \( S \).

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