
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 square in the diagram is divided into 9 identical smaller squares, and they have a total of 16 vertices (common vertices counted as one). Using 3 points that are not collinear among them as vertices, triangles can be formed. Among these triangles, how many have the same area as the shaded triangle?

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