
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
Points $P$ and $Q$ lie on line segment $\overline{ST}$. The length of $\overline{SP}$ is $5$ times the length of $\overline{PT}$, and the length of $\overline{SQ}$ is $7$ times the length of $\overline{QT}$. The length of $\overline{PQ}$ is what fraction of the length of $\overline{ST}$?
A) $\frac{1}{24}$
B) $\frac{1}{20}$
C) $\frac{1}{5}$
D) $\frac{1}{30}$

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