
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
Quadrilateral $PQRS$ has right angles at $Q$ and $R$, triangles $PQR \sim QRS$, and $PQ > QR$. Inside $PQRS$ lies point $T$ such that $PQR \sim RTQ$ and the area of $\triangle PTS$ is $25$ times the area of $\triangle RTQ$. What is $\tfrac{PQ}{QR}$?

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