
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

Prokop constructed a triangle \(ABC\), where the internal angle at vertex \(A\) was greater than \(60^{\circ}\) and the internal angle at vertex \(B\) was less than \(60^{\circ}\). Jirka drew a point \(D\) in the half-plane bounded by line \(AB\) and point \(C\), in such a way that triangle \(ABD\) was equilateral. The boys then discovered that triangles \(ACD\) and \(BCD\) are isosceles with the principal vertex at \(D\).

Determine the measure of angle \(ACB\).

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