
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 late ancient Greece, the mathematician Pappus explored the properties of the focus and directrix of conic sections in his "Collection of Mathematics": the locus of all points in a plane that are at a constant ratio of distances from a certain point and a fixed line is a conic section. This is the second definition or unified definition of conic sections. If the ratio of the distance from a moving point $P\left(x,y\right)$ in the plane to the fixed point $A\left(1,0\right)$ and to the fixed line $x=9$ is $\frac{1}{3}$, then the equation of the locus of point $P$ is ______.

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