
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
In the coordinate plane, a point is called an integer point if both its x-coordinate and y-coordinate are integers. For any natural number \( n \), the point \( O \) (the origin) is connected to the point \( A_n(n, n+3) \). Let \( f(n) \) denote the number of integer points on the line segment \( OA_n \) excluding the endpoints. Find the value of \( f(1) + f(2) + \cdots + f(1990) \).

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