
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, one polygon is a square and the other is a regular pentagon. What is the value, in degrees, of the sum of the measures of angles $ABC$ and $ABD$, assuming $AB$ is a common side between the square and pentagon?

[asy]
draw(10dir(45)--10dir(135)--10dir(225)--10dir(315)--cycle,linewidth(2));
draw(10dir(315)--10dir(348)--10dir(21)--10dir(63)--10dir(105)--cycle,linewidth(2));

label("A",10dir(315),S);
label("B",10dir(348),E);
label("C",10dir(45),N);
label("D",10dir(21),NE);
[/asy]

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