
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 this diagram, both polygons are regular. What is the value, in degrees, of the sum of the measures of angles $ABC$ and $ABD$?

[asy]
draw(10dir(0)--10dir(45)--10dir(90)--10dir(135)--10dir(180)--10dir(225)--10dir(270)--10dir(315)--10dir(360)--cycle,linewidth(2));
draw(10dir(225)--10dir(270)--10dir(270)+(0,-10)--10dir(225)+(0,-10)--10dir(225)--cycle,linewidth(2));

draw(10dir(270)+(-1,0)..9dir(270)..10dir(270)+dir(45),linewidth(2));
draw(10dir(270)+(-1.5,0)..10dir(270)+1.5dir(-135)..10dir(270)+(0,-1.5),linewidth(2));

label("A",10dir(225),W);
label("B",10dir(270),E);
label("C",10dir(0),E);
label("D",10dir(270)+(0,-10),E);

draw(10dir(270)+2dir(-135)--10dir(270)+dir(-135),linewidth(2));
[/asy]

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