
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 the point $P(x_{0}, y_{0})$ and the line $y=kx+b$, the distance from point $P$ to the line $y=kx+b$ can be calculated using the formula $d=\frac{{|kx_{0}-y_{0}+b|}}{{\sqrt{1+k^{2}}}}$.

For example, find the distance from point $P(-1,2)$ to the line $y=3x+7$.

**Solution:** Because the line is $y=3x+7$, where $k=3$ and $b=7$.
Therefore, the distance from point $P(-1,2)$ to the line $y=3x+7$ is: $d=\frac{{|3×(-1)-2+7|}}{{\sqrt{1+3^{2}}}}=\frac{2}{{\sqrt{10}}}=\frac{{\sqrt{10}}}{5}$.

Based on the above, answer the following questions:

1. Find the distance from point $P(2,-3)$ to the line $y=-x+3$.
2. Given that the center of circle $Q$ is at $(0,5)$ and the radius $r$ is $2$, determine the positional relationship between circle $Q$ and the line $y=\sqrt{3}x+9$ and explain the reason.
3. Given that the lines $y=-3x-2$ and $y=-3x+6$ are parallel, find the distance between these two lines.

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