
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
In the Cartesian coordinate system, consider the set of points \((x, y)\) that satisfy \(x < y\), \(|x| < 3\), and \(|y| < 3\) such that the equation \((x^3 - y^3) t^4 + (3x + y) t^2 + \frac{1}{x - y} = 0\) has no real roots. Let this set of points be denoted by \(N\). Find the area of the region formed by the set of points \(N\).

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