
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 $x O y$, a circle $\odot M$ is centered at $M(0,1)$ and intersects the parabola $y=x^{2}$ at points $A$, $B$, $C$, and $D$.

1. Find the range of values for the radius $r$ of $\odot M$.
2. Find the maximum area of the quadrilateral $ABCD$ (accurate to $10^{-4}$).

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