
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
For each positive integer \( n \), there is a circle around the origin with radius \( n \). Rainbow Dash starts off somewhere on the plane, but not on a circle. She takes off in some direction in a straight path. She moves \(\frac{\sqrt{5}}{5}\) units before crossing a circle, then \(\sqrt{5}\) units, then \(\frac{3 \sqrt{5}}{5}\) units. What distance will she travel before she crosses another circle?

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