
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 a new set \{4, 7, 8, 11\}. A number \( n \), not present in the set, is added such that the median and mean of the enlarged set become equal. What is the sum of all possible values of \( n \)?
A) 15.5
B) 20.5
C) 22.5
D) 23.5
E) 25.5

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