
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
Two congruent parallelograms have equal sides parallel to each other. In both parallelograms, we mark the vertices, the midpoints of the sides, and the intersection point of the diagonals. We choose one point from the marked points of the first parallelogram and another point from the marked points of the second parallelogram in every possible way, and construct the midpoint of the segment connecting the two chosen points.

How many different midpoints do we get in this way?

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