
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 list of numbers \[8, 3, x, 3, 7, 3, y\]. When the mean, median, and mode of this list are arranged in increasing order, they form a non-constant arithmetic progression. What is the sum of all possible values of \(y\) if \(x=6\)?
A) $\frac{51}{13}$  
B) $33$  
C) $\frac{480}{13}$  
D) $40$  
E) $34$

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