
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 that point A is a fixed point on the circle O with equation $x^2 + y^2 = 4$, and point B is a moving point on the circle O. If it satisfies $|\vec{AO} + \vec{BO}| = |\vec{AO} - \vec{BO}|$, then the value of $\vec{AO} \cdot \vec{AB}$ is __________.

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