
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 \( T \) be a set of \( 7 \) integers taken from \( \{1, 2, \dots, 15\} \) with the properties that if \( x \) and \( y \) are elements of \( T \) with \( x < y \), then \( y \) is not a multiple of \( x \), and at least three numbers in \( T \) must be prime. What is the least possible value of an element in \( T \)?
**A)** 2  
**B)** 3  
**C)** 4  
**D)** 5  
**E)** 7

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