
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
Consider the set $\{4, 7, 8, 12\}$ augmented by a fifth element $m$, not equal to any of the other four. The median of the resulting set is equal to its mean. What is the sum of all possible values of $m$?
A) 11
B) 13
C) 15
D) 17
E) 19

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