
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 two circles, $\odot A: x^2 + y^2 = 1$ and $\odot B: (x-3)^2 + (y-4)^2 = 4$, and a moving point $P$ in the plane. Tangents are drawn from $P$ to $\odot A$ and $\odot B$, touching them at points $D$ and $E$, respectively. If $PE = PD$, find the minimum distance from $P$ to the origin.

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