
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
The large square grid is composed of 81 small squares, each with an area of 1 square centimeter. Points $B$ and $C$ are two grid points. If you need to mark a point $A$ on one of the other grid points so that the area of $\triangle ABC$ is exactly 3 square centimeters, determine the number of such points $A$.

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