
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
The set $\{2, 5, 8, 11\}$ is increased by adding a new element $m$, not already in the set, such that the median of the new set equals its mean. What is the sum of all possible values of $m$?
A) 10 
B) 12
C) 13
D) 14
E) 15

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