
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
Let  $f(n) = \sum^n_{d=1} \left\lfloor \frac{n}{d} \right\rfloor$  and  $g(n) = f(n) -f(n - 1)$ . For how many  $n$  from  $1$  to  $100$  inclusive is  $g(n)$  even?

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