
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 the diagram, a regular octagon has a square inside it, sharing one side with the octagon. Determine the degree measure of $\angle XYZ$ in the configuration where $X, Y, Z$ are consecutive vertices with $Y$ and $Z$ on the square, and $X$ on the octagon.

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