
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 ellipse C: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a＞b＞0)$$ with its right focus at F(1, 0), and the point (-1, $$\frac { \sqrt {2}}{2}$$) lies on the ellipse C.  
(1) Find the standard equation of the ellipse C;  
(2) Given a moving line l passing through point F, and intersects with ellipse C at points A and B, is there a fixed point Q on the x-axis such that $$\overrightarrow {QA}\cdot \overrightarrow {QB}=- \frac {7}{16}$$ always holds? 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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