
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
From a point on the Earth's surface, a large number of small balls are launched in all directions with the same speed of 10 m/s. Among all the balls that fall at a distance not closer than 96% of the distance reached by the farthest ball, find the one that will be in flight for the longest time.

What is this time? Give the answer in seconds, rounded to one decimal place. The acceleration due to gravity is \(10 \mathrm{~m} / \mathrm{c}^{2}\).

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