
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
A trapezoid has bases of 3 and 9, and legs of 4 and 6. A line parallel to the bases divides the trapezoid into two smaller trapezoids with equal perimeters. Determine the ratio in which this line divides one of the legs.

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