
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 a line passing through point $A(-2,0)$ intersects with the line $x=2$ at point $C$, and a line passing through point $B(2,0)$ intersects with $x=-2$ at point $D$. If line $CD$ is tangent to the circle $x^{2}+y^{2}=4$, then the equation of the trajectory of the intersection point $M$ of lines $AC$ and $BD$ is ______.

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