
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 rectangle with diagonals and segments joining the midpoints of opposite sides. Let the rectangle have different length sides, and the diagonals intersect at the center. Calculate the total number of triangles of any size formed by this configuration.

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