Which season is your favourite season, spring, summer, autumn or winter? I like autumn best. Autumn is the time for harvest(收获). In autumn I can eat many different fruits：apples, pears, grapes and so on. I can also eat fresh vegetables. Autumn is cool. I feel comfortable(舒适的). I am happy to see the leaves turn red and yellow.

已知函数$f\left(x\right)={\cos }^{2}x+2\sqrt{3}\sin x\cos x-{\sin }^{2}x$．

（1）求函数f（x）的最小正周期及单调增区间；

（2）在△ABC中，A、B、C所对的边分别为a，b，c，若a=$\sqrt{3}$，f（A）=1，求b+c的最大值．