
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
If circle $O_1: x^2+y^2=5$ and circle $O_2: (x+m)^2+y^2=20$ ($m \in \mathbb{R}$) intersect at points $A$ and $B$, and the tangents to the circles at point $A$ are perpendicular to each other, then the length of segment $AB$ is ______.

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