
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 the circle M: $$(x+ \sqrt {5})^{2}+y^{2}=36$$, and a fixed point N($$\sqrt {5}$$,0), let P be a moving point on circle M, and point Q lies on NP, point G lies on MP, satisfying $$\overrightarrow {NP}=2 \overrightarrow {NQ}$$, $$\overrightarrow {GQ}\cdot \overrightarrow {NP}=0$$.
(1) Find the equation of the trajectory C of point G;
(2) A line l with slope k passes through point (2,0) and intersects curve C at points A and B. Let O be the origin. Is there such a line l that makes $$\overrightarrow {OA}\cdot \overrightarrow {OB}$$≤-1? If it exists, find the range of values for the slope k; if not, explain why.

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