
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 $\Delta XYZ$, $XY = YZ$, $m\angle FZY = 30^{\circ}$, and $FZ \parallel XY$. Determine the measure of $m\angle GFZ$.

[asy] pair X,Y,Z,F,G; Y = dir(-30); X = dir(-150); F = (.5,0); G = .4 * dir(30);
draw(Z--Y--X--G,EndArrow); draw(Z--F,EndArrow);
label("$X$",X,W); label("$Y$",Y,NW);label("$Z$",Z,E);label("$F$",F,E);label("$G$",G,E);
[/asy]

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