
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
Given a quadrilateral $ABCD$ where the internal angles form an arithmetic progression, the angles are such that $\angle ADB$ is double the $\angle DBA$. Triangles $ABD$ and $DCB$ are similar with $\angle DBA = \angle DCB$ and $\angle ADB = \angle CBD$. Furthermore, the angles within triangle $ABD$ form an arithmetic progression as well. Find the sum of the two smallest angles in $ABCD$.

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