
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 quadrilateral \(ABCD\), points \(X, Y, Z\) are the midpoints of segments \(AB, AD, BC\), respectively. It is known that \(XY\) is perpendicular to \(AB\), \(YZ\) is perpendicular to \(BC\), and the measure of angle \(ABC\) is \(100^\circ\). Find the measure of angle \(ACD\).

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