
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
Let the bases of the trapezoid \(ABCD\) be \(a\) and \(b\), respectively, and let \(O\) be the center of gravity of the trapezoid. In what ratio does point \(O\) divide the segment connecting the midpoints of the bases of the trapezoid?

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