
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 rectangular coordinate system, $O$ is the origin, $A(2,0)$, $B(0,2)$, and the moving point $P$ satisfies $| \overrightarrow{AP}|=1$, calculate the maximum value of $| \overrightarrow{OP}+ \overrightarrow{OB}|$.

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