
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 triangle $ABC$, a point $D$ is placed inside such that lines $AD$, $BD$, and $CD$ are drawn creating three new triangles. Points $E$ and $F$ lie on $AD$ and $CD$ respectively, creating three additional angles $x$ at $E$, $y$ at $F$ ($E$ and $F$ angles towards $B$), and $z$ at $B$ between line segments $BE$ and $BF$. What is the relation between these angles?
A) $x + y = 180^\circ$
B) $y + z = 180^\circ$
C) $x + z = 180^\circ$
D) $x + y + z = 180^\circ$
E) $x + y + z = 360^\circ$

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