
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 $l_1$:
\[\begin{cases} x=1+t \\ y=-5+ \sqrt{3}t \end{cases}\] where $t$ is a parameter, and line $l_2$: $x-y-2\sqrt{3}=0$ intersect at point $P$.

(1) Find the coordinates of point $P$;  
(2) Find the distance between point $P$ and $Q(1,-5)$.

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