
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 speeds of the first and second balls are \( v_{1} = v_{2} = 0.5 \mathrm{~m/s} \), and the speeds of the others are \( v_{3} = v_{4} = v_{5} = 0.3 \mathrm{~m/s} \). The initial distances between the balls are all equal to \( l = 1 \mathrm{~m} \). All collisions are perfectly elastic. After what time will the last collision occur in this system?

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