
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}:{{\left( x+m \right)}^{2}}+{{y}^{2}}=20\\) (where \\(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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