
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 $\Delta XYZ$, $XZ = YZ$, $m\angle DYZ = 50^{\circ}$, and $DY \parallel XZ$. Determine the number of degrees in $m\angle FDY$.

[asy] pair X,Y,Z,D,F; Y = dir(-50); X = dir(-130); D = (.5,0); F = .4 * dir(50);
draw(Z--Y--X--F,EndArrow); draw(Z--D,EndArrow);
label("$X$",X,W); label("$Z$",Z,NW);label("$Y$",Y,E);label("$D$",D,E);label("$F$",F,E);
[/asy]

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