
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
Points were marked on the sides of triangle \(ABC\): 12 points on side \(AB\), 9 points on side \(BC\), and 10 points on side \(AC\). None of the vertices of the triangle are marked. How many triangles can be formed with vertices at the marked points?

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