
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 potential real values of $x$ such that when the mean, median, and mode of the list
\[12, 3, 6, 3, 8, 3, x, 15\]
are arranged in increasing order, they form a non-constant arithmetic progression.
A) $\frac{150}{7}$ 
B) $\frac{170}{7}$
C) $\frac{190}{7}$
D) $\frac{204}{7}$
E) $\frac{220}{7}$

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