
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 trapezium $ABCD$, where $AB \parallel CD$ and $AB \neq CD$, the internal angles of $ABCD$ form a different arithmetic progression. Moreover, triangles $ABD$ and $DCB$ are similar with $\angle DBA = \angle DCB$, and $\angle ADB = \angle CBD$. Also, the angles in each of these two triangles form a modified arithmetic progression. If the sum of the internal angles of any quadrilateral remains $360^\circ$, and the smallest angle of the quadrilateral is $35^\circ$, what is the largest possible sum of the two largest angles of $ABCD$?
A) 240  
B) 245  
C) 250  
D) 253.33  
E) 260

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