
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]


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From a point located on the surface of the Earth, a large number of small balls are launched in all directions with a uniform speed of $10 \mathrm{m} / \mathrm{s}$. Among all the balls that have fallen at a distance no less than $96\%$ of the distance at which the farthest ball lands, find the one that will be in flight for the longest time. What is this time? Express your answer in seconds and round to one decimal place. The acceleration due to gravity is $10 \mathrm{~m} / \mathrm{s}^{2}$.

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