
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
Given one hundred numbers: \(1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots, \frac{1}{100}\). Calculate 98 differences: \(a_{1}=1-\frac{1}{3}, a_{2}=\frac{1}{2}-\frac{1}{4}, \ldots, a_{98}=\frac{1}{98}-\frac{1}{100}\). What is the sum of all these differences?

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