
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
A particle moves such that its speed starting from the third mile varies inversely with the square of the integral number of miles already traveled plus 1. Given that the third mile is traversed in 3 hours, determine the time, in hours, required to traverse the nth mile, where n ≥ 3.

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