
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
Triangle $PQR$ has $PQ=24$, $PR=26$, and $QR=30$. Points $M$ and $N$ are located on $\overline{PQ}$ and $\overline{PR}$, respectively, such that $\overline{MN}$ is parallel to $\overline{QR}$ and passes through the midpoint of the height from $P$ to $\overline{QR}$. Then $MN=\frac{a}{b}$, where $a$ and $b$ are coprime positive integers. Find $a+b$.

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