
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 line $l\_1$: $y=k(x+1)+2$, $(k∈R)$ passes through point $P$.
(1) Find the coordinates of point $P$;
(2) If line $l\_1$ is parallel to line $l\_2$: $3x-(k-2)y+5=0$, find the value of $k$ and then find the distance between the two lines.

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