
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
Given the line $mx - ny = 4$ and the circle $x^2 + y^2 = 4$ have no intersection points, determine the maximum number of intersection points between the line passing through point $P(m, n)$ and the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$.

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