
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 an ellipse C with its center at the origin of the Cartesian coordinate system xOy, and its foci on the x-axis, the distances from one of its vertices to the two foci are 7 and 1, respectively.  
(1) Find the equation of ellipse C;  
(2) If P is a moving point on ellipse C, and M is a point on the line passing through P and perpendicular to the x-axis, with $$\frac {|OP|}{|OM|} = \lambda$$, find the equation of the trajectory of point M, and describe what kind of curve this trajectory is.

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