
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 system, given point P (1, -1), draw the tangent line to the parabola $T_0$: $y=x^2$ at point P, and let the tangent points be M ($x_1$, $y_1$) and N ($x_2$, $y_2$) (where $x_1 < x_2$).  
(1) Find the values of $x_1$ and $x_2$;  
(2) If a circle with point P as its center is tangent to line MN, find the area of the circle.

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