
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 that the line \( l \), tangent to the circle \( x^2 + y^2 = 4 \), intersects the curve \( C: x^2 - \frac{y^2}{4} = 1 \) (where \( x > 0 \)) at two distinct points \( M \) and \( N \), find the equation of the locus of the intersection point of the tangents to the curve \( C \) at points \( M \) and \( N \).

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