
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 triangle \( OAB \) is drawn, where the intersection point of the medians is at the point \(\left(\frac{19}{3}, \frac{11}{3}\right)\), and points \(A\) and \(B\) have natural coordinates. Find the number of such triangles. (Here \(O\) denotes the origin - the point \((0,0)\); two triangles with the same set of vertices are considered the same, i.e., \(OAB\) and \(OBA\) are considered the same triangle.)

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