
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 two circles $⊙O\_1$: $x^{2}+y^{2}=5$ and $⊙O\_2$: $(x-m)^{2}+y^{2}=20 (m∈R)$, they intersect at points $A$ and $B$. The tangents of the two circles at point $A$ are perpendicular to each other. The length of line segment $AB$ is _____.

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