
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
Pictured below is a rectangular array of dots with the bottom left point labelled \( A \). In how many ways can two points in the array be chosen so that they, together with point \( A \), form a triangle with positive area?

[Image of a rectangular array of dots with point \( A \) at the bottom left.]

(Note: Include the actual image if providing this to an end-user, as visual context is critical for solving the problem).

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