
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
Triangles $ABC$ and $DBC$ are isosceles with $AB=BC$ and $DB=DC$. Point $D$ is on side $AC$ of $\triangle ABC$, $\angle ABC = 30^\circ$, and $\angle DBC = 110^\circ$. What is the degree measure of $\angle BAD$?

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