
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
Let $P$ be a moving point on the line $3x - 4y + 11 = 0$. A circle $C$: $x^2 + y^2 - 2x - 2y + 1 = 0$ is drawn with $P$ as its center. The circle intersects the line at points $A$ and $B$. Find the minimum area of the quadrilateral $PACB$.

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