
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 total number of triangles of any size in the configuration formed by drawing line segments from each vertex of the square to the midpoint of the adjacent sides, including the square's sides.

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