
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 right $\triangle PQR$ with $PQ = 6$, $QR = 8$, and $PR = 10$. A square $LMNO$ is inscribed in $\triangle PQR$ such that $L$ and $M$ are on $\overline{PR}$, $N$ on $\overline{PQ}$, and $O$ on $\overline{QR}$. Determine the side length of the square $LMNO$.

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