
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
On the graph $O:x^{2}+y^{2}=4$, there are two fixed points $A(\sqrt{2},\sqrt{2})$, $B(-\sqrt{2},\sqrt{2})$, and two moving points $C$, $D$, with $\overrightarrow{OC}⋅\overrightarrow{OD}=2$. Find the maximum value of $\overrightarrow{CA}⋅\overrightarrow{CB}+\overrightarrow{DA}⋅\overrightarrow{DB}$.

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