
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 an equilateral triangle \(ABC\), points \(D\) and \(E\) are fixed on sides \(AB\) and \(BC\) respectively, such that \(\overline{AD} = \overline{BE}\).

If segments \(AE\) and \(CD\) intersect at point \(P\), determine \(\measuredangle APC\).

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