
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 $C$ is defined by the equation ${(x-3)}^{2}+{(y-4)}^{2}=4$. A point $P(x,y)$ outside the circle is connected to the circle by a tangent line, with the tangent point being $Q$. If the length of the tangent line is equal to the distance from point $P$ to the origin $O$, determine the minimum value of $|PQ|$.

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