
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
The internal angles of quadrilateral $ABCD$ form an arithmetic progression. Triangles $ABD$ and $DCB$ are congruent right triangles with $\angle ABD = \angle CBD$ and $\angle ADB = \angle BDC$. Moreover, the angles in triangle $DAB$ and $BCD$ also form an arithmetic progression. Find the largest possible sum of the two largest angles of $ABCD$.

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