
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, points whose x-coordinates and y-coordinates are both integers are called lattice points. For any natural number \( n \), let \( O \) be the origin and \( A_{n}(n, n+3) \) be a point. Denote by \( f(n) \) the number of lattice points on the line segment \( OA_{n} \) excluding the endpoints. What is the value of \( f(1) + f(2) + \cdots + f(1990) \)?

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