
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 \( (\sqrt{3}, m) \) and \( (\sqrt{3}, n) \) are distinct points on the graph of \( y^2 + 3\sin(x^2) = 3x^2 y -2 \). What is \( |m-n| \)?
A) \( \sqrt{65} \)
B) \( \sqrt{73 - 12\sin(3)} \)
C) \( \sqrt{70} \)
D) \( \sqrt{75} \)

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