
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
In the Cartesian coordinate plane $(xOy)$, points $A$ and $B$ lie on the $x$-axis and $y$-axis, respectively, with $AB = 2$. If point $P$ has coordinates $(2, \sqrt{5})$, find the range of values for $| \overrightarrow{AP} + \overrightarrow{BP} + \overrightarrow{OP} |$.

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