
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, points \( B \) and \( C \) lie on \( AD \) and point \( E \) lies on \( CF \). The measures of four angles are shown. What is the value of \( x + y + z \)? 

![Diagram](https://cdn.mathpix.com/cropped/2024_04_17_2efeb2001664c4e9869eg-1.jpg?height=429&width=656&top_left_y=1268&top_left_x=797)

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