
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 diagram, one polygon is a regular pentagon and another is a regular octagon. Calculate the sum of the measures of angles $ABC$ and $ABD$, where:
- $A$ and $B$ are common vertices of the pentagon and octagon.
- $C$ is a vertex of the pentagon not shared with the octagon.
- $D$ is a vertex of the octagon not shared with the pentagon.

[Insert appropriate diagram here]

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