
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 xy-plane of the Cartesian coordinate system, there are points O(0,0) and A(0,1). A moving point M(x,y) has a projection point N on the x-axis, and the following relationship holds: $$\overrightarrow {MA}\cdot \overrightarrow {MO}= \overrightarrow {MO}\cdot \overrightarrow {MN}$$.
(1) Find the trajectory equation of the moving point M;
(2) A line passing through the point $$T(0,-\frac{1}{4})$$ intersects the trajectory of point M at points P and Q. If $$\overrightarrow {TQ}=3 \overrightarrow {TP}$$, find the equation of the line (express the result in slope-intercept form).

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