
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
The line $mx+ny-3=0$ and the circle $x^2+y^2=3$ have no common points. If the coordinates of point P are $(m, n)$, then a line passing through point P will have \_\_\_\_\_\_ common points with the ellipse $\frac{x^2}{7} + \frac{y^2}{3} = 1$.

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