
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 $\triangle PQR$, point $T$ is on side $QR$ at some point such that $QT = 3$ and $TR = 9$. Point $S$ is on $TR$ such that $TS = 7$ and $SR = 2$. What is the ratio of the area of $\triangle PQT$ to the area of $\triangle PTS$?

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