
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 $A$ and $B$ are moving points on the circle $C\_1:x^{2}+y^{2}=1$, with $AB= \sqrt {3}$, and $P$ is a moving point on the circle $C\_2:(x-3)^{2}+(y-4)^{2}=1$, determine the range of values for $| \overrightarrow{PA}+ \overrightarrow{PB}|$.

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