
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
Determine the sum of all possible values of $x$ such that the mean, median, and mode of the list 
\[9, 3, 5, 3, 7, 3, x, 11\] 
are in non-constant arithmetic progression when listed in increasing order.
A) 9
B) 17
C) 23
D) 47
E) 53

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