A physical system in three spatial coordinates \((x,y,z)\) is described by the following Lagrangian:

\[\large{L = x^2 \dot{y} + 2 z^3 \dot{x} \, \dot{y}^2 + 3 x \dot{x} \dot{z}} \]

Which quantity **must** be conserved?

**Details and Assumptions:**

- The dot convention denotes time differentiation

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