
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 at $D(0,0)$, $E(0,20)$, $F(30,0)$, $D'(-26,23)$, $E'(-46,23)$, and $F'(-26,-7)$. A rotation of $n$ degrees counterclockwise around the point $(x,y)$, where $0<n<180$, will transform $\triangle DEF$ to $\triangle D'E'F'$. Find $n+x+y$.

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