
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
A circle, whose center lies on the line \( y = b \), intersects the parabola \( y = \frac{12}{5} x^2 \) at least at three points; one of these points is the origin, and two of the remaining points lie on the line \( y = \frac{12}{5} x + b \). Find all values of \( b \) for which this configuration is possible.

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