
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 has its center on the parabola $y^2 = 16x$, and the circle passes through both the vertex and the focus of the parabola. If the center of the circle is in the first quadrant, find the standard equation of the circle.

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