Let \( (\hat{\mathrm{p}} \times \overrightarrow{\mathrm{q}}) \times \hat{\mathrm{p}}+(\hat{\mathrm{p}} \cdot \overrightarrow{\mathrm{q}}) \overrightarrow{\mathrm{q}}=\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right) \)
\( \mathrm{P} \)
\( \mathrm{W} \) \( \overrightarrow{\mathrm{q}}+(14-4 \mathrm{x}-6 \mathrm{y}) \hat{\mathrm{p}} \), where \( \hat{p} \) and \( \vec{q} \) are noncollinear vectors ( \( \mathrm{p}^{\wedge} \) is a unit vector) and \( \mathrm{x}, \mathrm{y} \) are scalars, then the value of \( x^{2}+y^{2} \) is equal to
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