
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
A set \{1,4,8\} is increased by adding one element \( x \), distinct from the existing elements. Determine \( x \) such that the median and mean of the new set are equal. What is the sum of all possible values of \( x \)?
A) 0
B) 5
C) 11
D) 13
E) 17

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