
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 a quadrilateral \(ABCD\) form an arithmetic progression. Triangles \(ABC\) and \(ADC\) are similar, and the angles of \(ABC\) are \(x\), \(x+10^\circ\), and \(x+20^\circ\). If the sum of the angles in each triangle is \(180^\circ\), and \(\angle BCD\) is the largest angle of \(ABCD\), determine the largest possible sum of the two largest angles of \(ABCD\).

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