赛瓦证明题

As shown in the figure, let $P$ be an arbitrary point inside $\mathrm{\Delta }ABC$ such that $\mathrm{\angle }CAL=\mathrm{\angle }PAB$, $\mathrm{\angle }MBC=\mathrm{\angle }PBA$, and $\mathrm{\angle }NCA=\mathrm{\angle }BCP$. Prove that the lines $AL$, $BM$, and $CN$ are concurrent.

如图，$P$ 是 $\mathrm{\Delta }ABC$ 内任意一点，满足 $\mathrm{\angle }CAL=\mathrm{\angle }PAB,\mathrm{\angle }MBC=\mathrm{\angle }PBA,\mathrm{\angle }NCA=\mathrm{\angle }BCP$，求证：$AL$、$BM$、$CN$ 三线共点.