
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
The arithmetic mean of two distinct integers $x$ and $y$ is 15, and their geometric mean plus 6 equals the arithmetic mean. Determine the absolute difference $|x - y|$.
A) 20
B) 24
C) 28
D) 32
E) 36

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