
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
Given rectangle $WXYZ$ with $WZ = 8$ and $ZX = 4$, points $P$ and $Q$ on side $ZX$ such that $ZP = PQ = QX$, and lines $\overline{WP}$ and $\overline{WQ}$ intersect diagonal $\overline{YZ}$ at points $R$ and $S$, respectively, find the ratio $ZR:RS:SY$.

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