
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]


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Given the equation of circle C is $x^2+y^2=1$, and the equation of line $l$ is $x+y=2$, find the minimum value of the absolute difference $|PA|$ between any point P on the circle and the point A where a line forming a 45° angle with line $l$ intersects line $l$.

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