
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
Points $( e, a)$ and $( e, b)$ are distinct points on the graph of $y^2 + x^3 = 2x y + 4$. What is $|a-b|$?
A) $2\sqrt{e^2 - e^3 + 2}$
B) $2e$
C) $2\sqrt{e^2 - e^3 + 4}$
D) $2(e-1)$
E) $4$

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