
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
In the Cartesian coordinate plane, given point $P(1,-1)$, a parabola $T_{0}$: $y=x^{2}$ is tangent to the line passing through point $P$ at points $M(x_{1},y_{1})$ and $N(x_{2},y_{2})$ ($x_{1} < x_{2}$).

(1) Find the values of $x_{1}$ and $x_{2}$;

(2) If a circle with center at point $P$ is tangent to line $MN$, find the area of the circle.

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