
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 point $P(a,-1)$ ($a\in R$), draw a tangent line from point $P$ to the parabola $C$: $y=x^{2}$, with the tangent points being $A(x_{1},y_{1})$ and $B(x_{2},y_{2})$ ($x_{1} < x_{2}$).

1. Find the values of $x_{1}$ and $x_{2}$ (express in terms of $a$);
2. If a circle $E$ with point $P$ as its center 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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