
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  $\triangle ABC$  and  $\triangle A'B'C'$  lie in the coordinate plane with vertices  $A(0,0)$ ,  $B(0,12)$ ,  $C(16,0)$ ,  $A'(24,18)$ ,  $B'(36,18)$ , and  $C'(24,2)$ . A rotation of  $m$  degrees clockwise around the point  $(x,y)$ , where  $0<m<180$ , will transform  $\triangle ABC$  to  $\triangle A'B'C'$ . Find  $m+x+y$ .

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