
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
A moving point P is on the circle $x^2+y^2=36$, and it is connected to a fixed point Q(4,0) with the midpoint of the line segment being M.  
(1) Find the equation of the trajectory of point M.  
(2) A line $l$ passing through the fixed point (0,-3) intersects the trajectory of point M at two distinct points A$(x_1,y_1)$ and B$(x_2,y_2)$, satisfying $\frac{x_1}{x_2} + \frac{x_2}{x_1} = \frac{21}{2}$. Find the equation of line $l$.

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