
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 augmented by a fifth element $n$, distinct from the others. The median of the new set should equal its mean. What is the sum of all possible values of $n$?
A) 14.5
B) 16.5
C) 18
D) 19.5
E) 20

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