
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
Lines $p$, $q$, and $r$ are parallel to each other. $m\angle P = 100^\circ$, and $m\angle Q = 130^\circ$. What is the number of degrees in $m\angle R$?

[asy]
size(200); real h = 1.2; real k = 2.4; currentpen = fontsize(10pt);
draw(Label("$p$",Relative(1)),(0,0)--(1,0),E);
draw(Label("$q$",Relative(1)),(0,-h)--(1,-h),E);
draw(Label("$r$",Relative(1)),(0,-k)--(1,-k),E);
draw((0,-h)--h/2*(cos(130*pi/180),sin(130*pi/180)) + (0,-h));
draw(Label("$R$",Relative(1)),(0,0)--h*sqrt(3)/2*(cos(-100*pi/180),sin(-100*pi/180)),W);
label("$P$",(0,0),N); label("$Q$",(0,-h),S); label("$S$",(0,-k),S);
label("$100^\circ$",(0,0),SE); label("$130^\circ$",(0,-h),NE);
[/asy]

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