
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
Define  $H_n = 1+\frac{1}{2}+\cdots+\frac{1}{n}$ . Let the sum of all  $H_n$  that are terminating in base 10 be  $S$ . If  $S = m/n$  where m and n are relatively prime positive integers, find  $100m+n$ .

*Proposed by Lewis Chen*

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