
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
Two regular polygons, a pentagon and an octagon, are placed such that they share one side. If $A$ is a vertex on the shared side belonging to both polygons, and $B$ and $C$ are adjacent vertices in the pentagon and $D$ an adjacent vertex in the octagon, compute the sum of the angles at $\angle BAC$ and $\angle BAD$.

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