
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
Draw a tangent line $PQ$ from a moving point $P$ to the circle: $(x-3)^{2}+(y-4)^{2}=1$, where $Q$ is the tangent point. If $|PQ|=|PO|$ ($O$ is the origin of coordinates), then the minimum value of $|PQ|$ is \_\_\_.

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