
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
You start with a regular pentagon \(A B C D E\). Then you draw two circles: one with center \(A\) and radius \(A B\), and the other with center \(B\) and radius \(B A\). Let the point inside the pentagon at which these two circles intersect be \(X\).
What is the size of \(\angle D E X\)?

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