
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 C: (x-2)²+(y-3)²=2, point M(-2, 1), and point P as any point outside the circle. A tangent line is drawn from point P to circle C, with the point of tangency being N. Point P satisfies |PM|=|PN|, forming a trajectory E. If point A moves along circle C and point B moves along trajectory E, what is the minimum value of |AB|?

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