6.(2023•广州二模)已知函数f(x)=sin(2x+φ)f(x)=\sin (2x+\varphi )f(x)=sin(2x+φ),若f(x)⩽∣f(π3)∣f(x)\leqslant \vert {f({\frac{\pi }{3}})}\vertf(x)⩽∣f(3π)∣恒成立,且f(π)>f(π4)f(\pi )>f({\frac{\pi }{4}})f(π)>f(4π),则f(x)f(x)f(x)的单调递增区间为((( )))