
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 coordinate plane, triangles $\triangle DEF$ and $\triangle D'E'F'$ have vertices $D(0,0)$, $E(0,15)$, $F(20,0)$, $D'(30,20)$, $E'(45,20)$, and $F'(30,0)$. A rotation of $n$ degrees clockwise around point $(x,y)$ transforms $\triangle DEF$ to $\triangle D'E'F'$. Determine the sum $n + x + y$ if $0 < n < 180$.

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