
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, the first polygon is a regular pentagon, and the second is a regular triangle. What is the value, in degrees, of the sum of the measures of angles $ABC$ and $ABD$?

[asy]
draw(10dir(18)--10dir(90)--10dir(162)--10dir(234)--10dir(306)--cycle,linewidth(2));  // Pentagon
draw(10dir(234)--10dir(306)--10dir(306)+(0,-10)--10dir(234)+(0,-10)--10dir(234)--cycle,linewidth(2));  // Triangle

label("A",10dir(234),W);
label("B",10dir(306),E);
label("C",10dir(18),E);  // A point on the pentagon
label("D",10dir(306)+(0,-10),E);  // A point on the triangle

draw(10dir(306)+2dir(-135)--10dir(306)+dir(-135),linewidth(2));
[/asy]

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