
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 $y^2 + x^4 = 2x^2y + 1$. What is $|a-b|$?
A) 1
B) $e$
C) 2
D) $\sqrt{1+e}$
E) 1 + $e$

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