
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 $ABCD$ be a convex quadrilateral, and let $M_{AB},$ $M_{BC},$ $M_{CD},$ $M_{DA}$ denote the midpoints of sides $AB,$ $BC,$ $CD,$ and $DA$, respectively. Find the ratio $\frac{[M_{AB} M_{BC} M_{CD} M_{DA}]}{[ABCD]}.$

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