
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 the line $y=kx+4-3k$ and the function $f(x)=\frac{4x-11}{x-3}$, their graphs intersect at points $A$ and $B$. Let $P(x,y)$ be a moving point on the plane such that $|\overrightarrow{PA}+\overrightarrow{PB}|=2$. Determine the range of values for $x^2+y^2$.

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