
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
Find the measure of $\angle FYD$, given that $\overline{AB} \parallel \overline{CD}$ and $\angle AXF = 130^\circ$, and $\triangle XFG$ is an isosceles triangle with $\angle FXG = 36^\circ$.

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