
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
Given $\triangle XYZ$ with side lengths $XY=13$, $YZ=14$, and $ZX=15$, and a median $\overline{XM}$, find the length of $RS$, where points $G$ and $F$ lie on sides $\overline{ZX}$ and $\overline{XY}$ respectively, such that $\overline{YG}$ and $\overline{ZF}$ are angle bisectors and intersect $\overline{XM}$ at points $R$ and $S$ respectively.

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