
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 five different positive integers, the largest of which is \( m \). It is impossible to construct a quadrilateral with non-zero area, whose side-lengths are all distinct elements of \( S \). What is the smallest possible value of \( m \)?  
A) 2  
B) 4  
C) 9  
D) 11  
E) 12

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