
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 $XYZ$, side $XZ = 600$ and side $ZY = 400$. Points $Q$ and $R$ are located on $\overline{XZ}$ and $\overline{XY}$ respectively, so that $XQ = QZ$, and $\overline{ZR}$ is the angle bisector of $\angle Z$. Point $S$ is the intersection of $\overline{YQ}$ and $\overline{ZR}$. Let $N$ be the point on line $YQ$ such that $Q$ is the midpoint of $\overline{SN}$. Given $XN = 300$, determine $RS$.

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