
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 running turtle moves in a straight line as follows. In the first segment of the path, which measures $\frac{1}{2} \text{ m}$, it runs at a speed of $3 \text{ m/s}$. In the second segment, which measures $\frac{1}{3} \text{ m}$, it runs at a speed of $4 \text{ m/s}$. In the third segment, which measures $\frac{1}{4} \text{ m}$, it runs at a speed of $5 \text{ m/s}$ and so on.

a) What is the time the turtle takes to cover the first segment? Write the result as the difference of two unit fractions, that is, fractions with numerator equal to 1.

b) Do the same for the second segment.

c) Calculate the time the turtle takes to cover the first 2013 segments.

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