Let \(ABC\) be an acute angled triangle in which \(D,E\) and \(F\) are points on \(BC,CA, AB \) respectively such that \(AD\) is perpendicular to \(BC,AE=EC\) and \(CF\) bisects \(\angle C\) internally. Suppose \(CF\) meets \(AD\) and \(DE\) in \(M\) and \(N\) respectively. If \(FM=2,MN=1,NC=3,\)find the perimeter of the triangle \(ABC\).

Submit your answer to two decimal places.

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