
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 $XYZ$, $\angle XYZ = 60^\circ$ and $\angle YXZ = 60^\circ$, with $XY = 1$. Let $N$ be the midpoint of $\overline{XY}$. Point $T$ lies on side $\overline{XZ}$ such that $\overline{YT}\perp\overline{ZN}$. Locate point $B$ such that line $TB$ is parallel to $ZY$ and $TB = 2 \cdot YZ$. Determine the length of $XB$ as a reduced fraction $\frac{p}{q}$, where $p$ and $q$ are coprime integers, and find $p+q$.

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