
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 point $P$ moves on the line $3x+4y+8=0$, and $PA$ and $PB$ are two tangent lines of the circle $x^{2}+y^{2}-2x-2y+1=0$ with $A$ and $B$ as the tangent points, and $C$ as the circle center. Find the minimum value of the quadrilateral $PACB$'s area.

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