
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 that $P$ is a moving point on the line $3x+4y+8=0$, and $PA$, $PB$ are tangents to the circle $x^2+y^2-2x-2y+1=0$ with $A$, $B$ being the points of tangency, and $C$ being the center of the circle. When the area of quadrilateral $PACB$ is minimized, the length of $AB$ is \_\_\_\_\_\_.

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