
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
As shown in the diagram, \(E, F, G, H\) are the midpoints of the sides \(AB, BC, CD, DA\) of the quadrilateral \(ABCD\). The intersection of \(BH\) and \(DE\) is \(M\), and the intersection of \(BG\) and \(DF\) is \(N\). What is \(\frac{S_{\mathrm{BMND}}}{S_{\mathrm{ABCD}}}\)?

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