
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 $\triangle XYZ$, $\angle XYZ = 105^\circ$ and $\angle YXZ = 30^\circ$. Point $A$ is the midpoint of $\overline{XZ}$. A point $B$ lies on side $\overline{YZ}$ such that $\overline{XB} \perp \overline{YA}$. Extend segment $\overline{YZ}$ through $Z$ to point $D$ such that $BD = 2AB$. Find the length of $YD$ if $YX = 2$ and express your answer in terms of trigonometric functions.

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