
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 a triangle \(ABC\) with \(\angle C = 120^{\circ}\). Point \(D\) is the foot of the perpendicular dropped from point \(C\) to side \(AB\); points \(E\) and \(F\) are the feet of the perpendiculars dropped from point \(D\) to sides \(AC\) and \(BC\) respectively. Find the perimeter of triangle \(ABC\) given that triangle \(EFC\) is isosceles and its area is \(\sqrt{3}\).

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