
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 circle C: (x-2√2)^2+(y-1)^2=1 and two points A(-t,0), B(t,0) where t > 0. If there exists a point P on circle C such that ∠APB=90°, calculate the minimum value of t.

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