
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 point P(a, -1) (a∈R), draw the tangent line to the parabola C: $y=x^2$ at point P, and let the tangent points be A($x_1$, $y_1$) and B($x_2$, $y_2$) (where $x_1<x_2$).

(Ⅰ) Find the values of $x_1$ and $x_2$ (expressed in terms of a);

(Ⅱ) If a circle E with center at point P is tangent to line AB, find the minimum area of circle E.

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