
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 $A(-1,2)$ and $B(0,1)$, and a moving point $P$ such that $|PA|= \sqrt {2}|PB|$.
(I) If the trajectory of point $P$ forms a curve $C$, find the equation of this curve.
(II) If point $Q$ lies on the line $l_{1}$: $3x-4y+12=0$, and line $l_{2}$ passes through point $Q$ intersecting curve $C$ at only one point $M$, find the minimum value of $|QM|$.

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