
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
Triangles $\triangle DEF$ and $\triangle D'E'F'$ lie in the coordinate plane with vertices $D(0,0)$, $E(0,20)$, $F(30,0)$, $D'(40,30)$, $E'(52,30)$, $F'(40,10)$. A rotation of $n$ degrees clockwise around the point $(p,q)$ where $0<n<180$, will transform $\triangle DEF$ to $\triangle D'E'F'$. Find $n+p+q$.

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