
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 larger base of a trapezoid is twice the length of its smaller base. A line parallel to the bases is drawn through the point of intersection of the diagonals. Find the ratio of the height of each of the two resulting trapezoids to the height of the original trapezoid.

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