
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 Cartesian coordinate system $xOy$, given points $A(1,0)$, $B(0,3)$, $C(3,0)$, and a moving point $P$ such that $|\overrightarrow{CP}|=1$, calculate the maximum value of $|\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OP}|$.

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