
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, a parabola given by \( y = kx^2 \) (where \( k > 0 \)) and a circle given by \( (x - a)^2 + (y - b)^2 = r^2 \) have at least 3 points in common. One of these points is the origin, and the other two points lie on the line \( y = kx + b \). What is the minimum value of the real number \( b \)?

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