
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 points $A$, $B$, and $C$ move on the unit circle $x^{2}+y^{2}=1$, and $AB \perp BC$, if the coordinates of point $P$ are $(2,0)$, then the range of values for $| \overline {PA}+ \overline {PB}+ \overline {PC}|$ is _______.

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