
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 system, $O$ is the origin, $A$ is $(-1,0)$, $B$ is $(0, \sqrt{3})$, $C$ is $(3,0)$, and the moving point $D$ satisfies $|CD|=1$. Find the maximum value of $|OA+OB+OD|$.

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