
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 pentagon $ABCDE$, the internal angles form two sets of arithmetic progressions with three angles in one progression and two in another. Specifically, $\angle ABC = \angle BCD = \angle CDE$ and $\angle EAB = \angle EDC$. If triangles $ABE$ and $CDE$ are similar and have their angles forming an arithmetic progression, what is the largest possible sum of the three largest internal angles of $ABCDE$?
A) 320°
B) 330°
C) 340°
D) 350°

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