
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 $\{4, 7, 15, 18\}$ is augmented by a fifth element $n$, not equal to any of the other four. The median of the resulting set and the mean are equal. Find the sum of all possible values of $n$.
A) 30
B) 38
C) 40
D) 42
E) 50

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