
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 fifth and a sixth number, $m$ and $n$, are added to the set $\{5, 8, 12, 15\}$ to make the mean of the set equal to its median. The number of possible integer values for $m$ and $n$ with $m \neq n$ and both numbers being distinct from the numbers already in the set, is?
A) 0  
B) 1  
C) 2   
D) 3  
E) More than 3

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