
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 whose x-coordinate and y-coordinate are both integers is called a lattice point. For any positive integer \( n \), connect the origin \( O \) with the point \( A_{n}(n, n+3) \). Let \( f(n) \) denote the number of lattice points on the line segment \( OA_{n} \) excluding the endpoints. Determine the value of \( f(1)+f(2)+\cdots+f(1990) \).

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