
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 midpoints of the non-parallel sides of a trapezoid and the midpoints of the diagonals lie on a line parallel to the base. The distance between the midpoints of the non-parallel sides is equal to half the sum of the lengths of the parallel sides, and the distance between the midpoints of the diagonals is equal to half the difference of the lengths of the parallel sides.

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