
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
Given an equilateral triangle \(ABC\). A line parallel to \(AC\) intersects lines \(AB\) and \(BC\) at points \(M\) and \(P\) respectively. Point \(D\) is the center of the equilateral triangle \(PMB\), and point \(E\) is the midpoint of segment \(AP\). Find the angles of triangle \(DEC\).

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