
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 circle $A$: $x^{2}+y^{2}=1$, and circle $B$: $(x-3)^{2}+(y+4)^{2}=10$, $P$ is a moving point on the plane. A tangent line is drawn from $P$ to circles $A$ and $B$, with the tangent points being $D$ and $E$, respectively. If $PE=PD$, find the minimum distance from point $P$ to the origin.

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