
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
Consider a square with an inscribed circle that touches the midpoints of each side of the square. The square also has its diagonals drawn, as well as the segments joining the midpoints of its opposite sides. Calculate the total number of triangles, of any size, formed within this configuration.

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