
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
Let $F$ be the midpoint of segment $A B$, and let $Z$ be an arbitrary point on segment $A F$. At point $F$, draw a perpendicular to $A B$ and mark a distance $F X = F A$ on it. Similarly, at point $B$, draw a perpendicular to $A B$ and mark a distance $B Y = A Z$ on it, such that $X$ and $Y$ are on the same side of the line $A B$. What is the measure of angle $X Z Y$?

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