
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
In the rectangular coordinate system $xoy$, the points on the curve $C\_1$ are outside the circle $C\_2$: $(x-5)^{2}+y^{2}=9$. For any point $M$ on $C\_1$, the distance from $M$ to the line $x=-2$ is equal to the minimum distance from that point to any point on the circle $C\_2$. Find the equation of the curve $C\_1$.

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