
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 function $f(x)$ is an increasing function on $\mathbb{R}$ and its graph is symmetric about the point $(3, 0)$, for real numbers $x$ and $y$ satisfying $f(x^2-2\sqrt{3}x+9)+f(y^2-2y)\leq 0$, the range of values for $\frac{y}{x}$ is ______.

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