
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 triangle $XYZ$ be a triangle where $XZ$ is the base and a circle with center $W$ inside it such that the circle is tangent to $XY$, $YZ$, and $XZ$. Given $\angle XYZ = 75^\circ$ and $\angle YXZ = 68^\circ$, find $\angle YWZ$, in which $W$ bisects $\angle XYZ$.

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