
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
Given the set $\{2, 5, 8, 11\}$, augmented by a fifth element $n$ not equal to any of the other four, find the sum of all possible values of $n$ such that the median and the mean of the resulting set are equal.
A) 18.5
B) 19.5
C) 20.5
D) 21.5
E) 22.5

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