
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 triangle \( XYZ \), \( XY = 14 \), \( YZ = 16 \), and \( ZX = 18 \). Point \( M \) is on \( \overline{XY} \), \( N \) is on \( \overline{YZ} \), and \( O \) is on \( \overline{ZX} \). Let \( XM = s \cdot XY \), \( YN = t \cdot YZ \), and \( ZO = u \cdot ZX \), where \( s \), \( t \), and \( u \) are positive and satisfy \( s + t + u = 3/4 \) and \( s^2 + t^2 + u^2 = 3/8 \). The ratio of the area of triangle \( MNO \) to the area of triangle \( XYZ \) can be written in the form \( a/b \), where \( a \) and \( b \) are relatively prime positive integers. Find \( a+b \).

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