
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 points $E(-2,0)$ and $F(2,0)$, and a moving point $M$ on curve $C$ such that $\overrightarrow{EM} \cdot \overrightarrow{FM} = -3$. Also given a fixed point $A(2,1)$, from a point $P(a, b)$ outside the curve $C$, a tangent line $PQ$ is drawn to the curve at point $Q$ such that $|PQ| = |PA|$.

(I) Find the equation of curve $C$.

(II) If a circle with center at point $P$ intersects with curve $C$, find the standard equation of the circle when its radius is at a minimum.

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