
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
For the parabola $C: y^2 = 4x$, we say that a point $M(x_0, y_0)$ is inside the parabola if $y_0^2 < 4x_0$. If point $M(x_0, y_0)$ is inside the parabola, find the number of common points between the line $l: y_0y = 2(x + x_0)$ and the curve $C$.

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