
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 a coordinate system, a circle with radius  $7$  and center is on the y-axis placed inside the parabola with equation  $y = x^2$  , so that it just touches the parabola in two points. Determine the coordinate set for the center of the circle.


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