\[ \large{\begin{cases} 3x+\{ y\} +\lfloor z \rfloor=23.3 \\ \lfloor x \rfloor +2y+\{ z\} =9.5 \\ 2\{ x\} +3\lfloor y \rfloor +z=14.1 \end{cases}}\]

Let \(x,y\) and \(z\) be real numbers, whose decimal part is formed by only one digit, satisfying the system of equations above. Find \(x+y+z\).

**Notations**:

- \( \lfloor \cdot \rfloor \) denotes the floor function.
- \( \lceil \cdot \rceil \) denotes the ceiling function.
- \( \{ \cdot \} \) denotes the fractional part function.

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