设$a\in R$$f\left(x\right)=\cos x(a\sin x-\cos x)+{\cos }^2(\frac{\pi }{2}-x)$满足$f(-\frac{\pi }{3})=f\left(0\right)$，求函数$f\left(x\right)$在$[\frac{\pi }{4},\frac{11\pi }{24}]$上的最大值和最小值．