
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
Triangle $XYZ$ is equilateral. Let $\overline{KL}$, $\overline{MN}$, and $\overline{OP}$ be three lines parallel to $\overline{YZ}$, splitting the height of triangle $XYZ$ into four equal segments with points $K$ and $L$ being closest to vertex $X$. If $XK = KM = MN = NP$, calculate the ratio of the area of trapezoid $OPYZ$ to the area of triangle $XYZ$.

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