
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 lengths of the sides of a trapezoid are 2, 10, 10, and 20. Find the length of the segment connecting the midpoints of the diagonals.

(It is known that these points are distinct). If there are multiple possible answers, list them in ascending order separated by commas or semicolons.

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