
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: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ ($a>b>0$) with an eccentricity of $$\frac {1}{2}$$, let A(0, b), B(a, 0), and F<sub>1</sub>, F<sub>2</sub> be the left and right foci of the ellipse, respectively, and the area of triangle △ABF<sub>2</sub> is $$\frac { \sqrt {3}}{2}$$.

(1) Find the equation of ellipse C;  
(2) A line passing through F<sub>1</sub> intersects with a parabola that has F<sub>2</sub> as its focus and its vertex at the origin at points P and Q. If $$\overrightarrow {F_{1}P}=\lambda \overrightarrow {F_{1}Q}$$ and $\lambda \in [2, 3]$, find the range of the area of triangle △F<sub>2</sub>PQ.

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