
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
The number of positive integers \( k \) such that there exists a pair of positive integers \( (a, b) \) satisfying
$$
\frac{k}{2015}(a+b)=\text{lcm}(a, b)
$$
where \(\text{lcm}(a, b)\) denotes the least common multiple of \(a\) and \(b\), is ______.

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