
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 with its center at the origin and foci on the x-axis and a focal distance of 2, and the length of the major axis is $$\sqrt {2}$$ times the length of the minor axis.
(1) Determine the standard equation of ellipse C.
(2) Let P(2, 0), a line l passing through the left focus F of the ellipse C intersects C at points A and B. If for any line l that satisfies these conditions, the inequality $$\vec{PA} \cdot \vec{PB} \leq \lambda (\lambda \in \mathbb{R})$$ always holds, find the minimum value of $$\lambda$$.

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