
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
On the coordinate plane, points whose x-coordinates and y-coordinates are both integers are called lattice points. For any natural number \( n \), connect the origin \( O \) with the point \( A_{n}(n, n+3) \). Let \( f(n) \) denote the number of lattice points on the 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}
user