
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 non-parallel sides of a trapezoid are extended until they intersect, and a line parallel to the bases of the trapezoid is drawn through this point of intersection. Find the length of the segment of this line that is limited by the extensions of the diagonals if the lengths of the bases of the trapezoid are $a$ and $b$.

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