
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 $\triangle PQR$, $P$ is the midpoint of $\overline{QR}$, $QP = 15$, and $PR = 20$. Let $T$ be on $\overline{PR}$, and $S$ be on $\overline{PQ}$, with $T$ externally dividing $\overline{PR}$ in the ratio 1:3. Let $U$ be the intersection of $\overline{ST}$ and $\overline{PM}$ where $M$ is the midpoint of $\overline{QR}$. Find the ratio $\frac{SU}{UT}$.

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