
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
When the mean, median, and mode of the list
\[4, 9, x, 4, 9, 4, 11, x\]
are arranged in increasing order, they form a non-constant geometric progression. What is the sum of all possible values of $x$?
A) 3
B) 6.83
C) 15.5
D) 17
E) 20

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