
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
Five identical balls roll on a smooth horizontal surface towards each other. The velocities of the first and second are $v_{1}=v_{2}=0.5$ m/s, and the velocities of the others are $v_{3}=v_{4}=v_{5}=0.1$ m/s. The initial distances between the balls are the same, $l=2$ m. All collisions are perfectly elastic. How much time will pass between the first and last collisions in this system?

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