
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(-4, 0), B(0, 4), C(1, 0), and A moving point D satisfies $|\overrightarrow{CD}|=1$. Calculate the maximum value of $|\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OD}|$.

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