
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
It is known that a moving point P and the two foci F<sub>1</sub>, F<sub>2</sub> of the hyperbola $$x^{2}- \frac {y^{2}}{3}=1$$ have a sum of distances greater than 4, which is a constant, and the maximum value of | $$\overrightarrow {PF_{1}}$$|•| $$\overrightarrow {PF_{2}}$$| is 9.
(1) Find the equation of the trajectory E of the moving point P;
(2) If A and B are two distinct points on curve E, and point M(0, 2) satisfies $$\overrightarrow {AM}$$ = λ $$\overrightarrow {MB}$$, find the range of the real number λ.

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