
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

Calculate the sum

$$
S=\frac{2015}{3 \cdot 8}+\frac{2015}{8 \cdot 13}+\frac{2015}{13 \cdot 18}+\ldots+\frac{2015}{2008 \cdot 2013}
$$

In the answer, indicate the remainder when the closest natural number to the obtained value of $S$ is divided by 5.

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