
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
Given that point C is above the x-axis, the circle C with center C is tangent to the x-axis at point A(1,0) and intersects with circle O: x²+y²=4 at points P and Q. If the length of PQ is $\frac{\sqrt{14}}{2}$, find the standard equation of circle C.

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