
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
The number  $S$  is the result of the following sum:  $1 + 10 + 19 + 28 + 37 +...+ 10^{2013}$ If one writes down the number  $S$ , how often does the digit ` $5$ ' occur in the result?

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