
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
Definition: The directed distance from point $M(x_{0},y_{0})$ to line $l$: $ax+by+c=0$ is $\dfrac {ax_{0}+by_{0}+c}{ \sqrt {a^{2}+b^{2}}}$. Given points $A(-1,0)$, $B(1,0)$, and line $m$ passes through point $P(3,0)$. If there exists a point $C$ on the circle $x^{2}+(y-18)^{2}=81$ such that the sum of the directed distances from points $A$, $B$, $C$ to line $m$ is $0$, then the range of values for the slope of line $l$ is \_\_\_\_\_\_.

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