
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 \\(⊙A\\): \\(x^{2}+y^{2}=1\\), and \\(⊙B\\): \\((x-3)^{2}+(y-4)^{2}=4\\), \\(P\\) is a moving point in the plane. Tangents to \\(⊙A\\) and \\(⊙B\\) are drawn from \\(P\\), touching \\(⊙A\\) and \\(⊙B\\) at \\(D\\) and \\(E\\) respectively. If \\(PE=PD\\), then the minimum distance from \\(P\\) to the origin is \_\_\_\_\_\_.

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