
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
In trapezoid \(ABCD\) with \(BC \parallel AD\), it is known that \(AD = 3 \cdot BC\). A line intersects the non-parallel sides of the trapezoid at points \(M\) and \(N\) such that \(AM:MB = 3:5\) and \(CN:ND = 2:7\). Find the ratio of the areas of quadrilaterals \(MBCN\) and \(AMND\).

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