
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 line $l_1$: $y=k(x+1)+2$, ($k\in\mathbb{R}$) passes through a fixed point $P$.
(1) Find the coordinates of the fixed 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 the distance between the two lines at this time.

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