
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
Suppose  $N$  is any positive integer. Add the digits of  $N$  to obtain a smaller integer. Repeat this process of digit-addition till you get a single digit numbem. Find the number of positive integers  $N \le 1000$ , such that the final single-digit number  $n$  is equal to  $5$ .
Example:  $N = 563\to (5 + 6 + 3) = 14 \to(1 + 4) = 5$  will be counted as one such integer.

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