
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 point $A$ is a fixed point on the circle $O: x^{2}+y^{2}=4$, and point $B$ is a moving point on the circle $O$. If it satisfies $| \overrightarrow{AO}+ \overrightarrow{BO}|=| \overrightarrow{AO}- \overrightarrow{BO}|$, then $\overrightarrow{AO} \cdot \overrightarrow{AB}=$ \_\_\_\_\_\_ .

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