\(\overrightarrow{MA}=-\frac{3}{4}\overrightarrow{BM}=\frac{3}{4}\overrightarrow{MB};\overrightarrow{AN}=-3\overrightarrow{CN}=3\overrightarrow{NC};\overrightarrow{CP}=\frac{1}{4}\overrightarrow{PB}\)
\(\overrightarrow{MA}+\overrightarrow{AN}=\frac{3}{4}\overrightarrow{MB}+3\overrightarrow{NC}\Leftrightarrow\overrightarrow{MN}=\frac{3}{4}\overrightarrow{MP}+\frac{3}{4}\overrightarrow{PB}+3\overrightarrow{NP}+3\overrightarrow{PC}\)
\(\Leftrightarrow\overrightarrow{MN}=\frac{3}{4}\overrightarrow{MP}+3\overrightarrow{CP}+3\overrightarrow{NP}-3\overrightarrow{CP}=\frac{3}{4}\overrightarrow{MP}+3\overrightarrow{NP}\)\(\Leftrightarrow\overrightarrow{MP}+\overrightarrow{PN}=\frac{3}{4}\overrightarrow{MP}+3\overrightarrow{NP}\)
\(\Leftrightarrow\frac{1}{4}\overrightarrow{MP}=4\overrightarrow{NP}\Leftrightarrow\overrightarrow{MP}=16\overrightarrow{NP}\Rightarrow\overline{M,N,P}\)
