
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
In the rectangular coordinate system xOy, the equation of line l is $y-2= \sqrt {3}(x+2)$, and line l intersects with curve C: $(y-2)^2-x^2=1$ at points A and B.
(1) Find the standard parametric equation of line l;
(2) Find the length of |AB|;
(3) Establish a polar coordinate system with O as the pole and the positive semi-axis of the x-axis as the polar axis. If the polar coordinates of point P are $(2 \sqrt {2}, \frac {3π}{4})$, find the distance from point P to the midpoint M of line segment AB.

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