
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 points M(4, 0), N(1, 0), if a moving point P satisfies $$\overrightarrow {MN} \cdot \overrightarrow {MP} = 6| \overrightarrow {NP}|$$.
(1) Find the trajectory C of the moving point P;
(2) Is there a point Q on curve C such that the area of △MNQ, $$S_{△MNQ}= \frac {3}{2}$$? If it exists, find the coordinates of point Q; if not, explain why.

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