
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 \( k(a) \) denote the number of points \((x, y)\) in the coordinate system such that \(1 \leq x \leq a\) and \(1 \leq y \leq a\) are relatively prime integers. Determine the following sum:

$$
\sum_{i=1}^{100} k\left(\frac{100}{i}\right)
$$

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