
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 for the third and subsequent miles varies inversely as the square of the integral number of miles already traveled. For each subsequent mile, the speed is constant. If the third mile is traversed in 4 hours, then the time, in hours, needed to traverse the $n$th mile is:
A) $(n-3)^2$
B) $(n-2)^2$
C) $(n-1)^2$
D) $n^2$
E) $2(n-2)^2$

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