
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 rocket moves so that its acceleration for the third and subsequent kilometers varies inversely as the square of the integral number of kilometers already traveled in total. If in reaching the third kilometer, the cumulative distance already traveled is $2$ km in $4$ hours, and the initial acceleration was constant, calculate the time in hours required to travel the $5^\text{th}$ kilometer.
A) 4 hours
B) 6 hours
C) 8 hours
D) 10 hours

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