
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's speed for the second and subsequent miles varies inversely as the square of the number of miles already traveled. The speed is constant for each subsequent mile. If the second mile is traversed in $2$ hours, determine the time, in hours, needed to traverse the $n$th mile.
A) $2n-1$
B) $2(n-1)^2$
C) $(n-1)^2$
D) $2n^2$

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