
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
Consider triangle $PQR$ with $PQ = 26$, $PR = 30$, and $QR = 28$. Points $S$ and $T$ are on line segments $\overline{PQ}$ and $\overline{PR}$, respectively, such that line segment $\overline{ST}$ is parallel to $\overline{QR}$ and contains the center of the inscribed circle of triangle $PQR$. Compute the length of $\overline{ST}$ and express your result as a fraction in its lowest terms, $a/b$. Find $a+b$.

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