Both Daoism and Zen meditation have profound influences in CMA.
Religions for the most part are subjective and personal.
Chinese culture has a lot of reasoning and logics into all of the above.
Some examples:
In Song dynasty, the wife of general Yang wanted to commit suicide after the husband was killed by some soldiers. The prince of Ging said no. She wanted to be faithful to her husband. Both live or both die. However, her husband just passed away, she did not finish grieving and burial. She actually was not faithful (Bu Chun). She was pregnant. If she did not deliver the baby and raise him, she was not pious. She ended the family of Yang.(Bu Xiao) She killed herself and the baby would die, too. She was not merciful for the baby. (Bu Ren) Most important of all, she did not avenge her husband death yet. She was not just. (Bu Yi)
She only thought about being faithful. However, Chun Xiao Ren Yi (Confuciaism) told her to think otherwise.
Both Daoism and Zen are always broadened by culture, science and knowledge into the "logics" of thinking and MA.
Buddha said do not say. (Fer So Bu Ge So)
You see things, you feel things, you hear things, you understand or appreciate things. When you try to describe them, your words may not completely represent the "truth". Oftentimes, words may be misleading or misunderstood.
You observe life and you experience life. When you try to say all the time, you are preoccupied, you may not see things clearly. Sometimes, it is better not to say or try to interprete things too early before you comprehand the events fully.
The best revelation in life is actually to experience. It is best not to say it.
On and on.
Before mixing any religions with CMA. There are all these logics of virtues (why and how) and reasonings including observations, science, physics etc. All these are part of study of CMA.
So Daoism and Zen may go as deep as you may.
Just a reminder for how Chinese think about life and MA.