
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 given diagram, there are two regular polygons, a pentagon and a square. Find the sum of the measures of angles \(ABC\) and \(ABD\) in degrees.

[asy]
draw(10dir(0)--10dir(72)--10dir(144)--10dir(216)--10dir(288)--cycle,linewidth(2));
draw(10dir(216)--10dir(288)--10dir(288)+(0,-10)--10dir(216)+(0,-10)--10dir(216)--cycle,linewidth(2));

label("A",10dir(216),W);
label("B",10dir(288),E);
label("C",10dir(0),E);
label("D",10dir(288)+(0,-10),E);
[/asy]

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