they live in the thick forest of high mountains there, ___ bamboo shoots and drinking spring water

eating bamboo shoots and drinking spring water
在这句中做伴随状语,
分词作状语的情况有两种,一种是主语(此句中是they)与分词(就是此句中的eat)是主动结构的,那么就用分词doing形式的
另一种是主语与分词成被动结构的(如:大楼被修好了),那么就用分词done形式的

现在分词做伴随状语时，这个分词的动作发出者就是主句中的主语
eating bamboo shoots and dringking spring water的动作发出者是句子的助于they。
例如，Coming into the room, I saw a girl crying.

不定式作状语
1.目的状语
He ran so fast as to catch the first bus. 他飞快地跑以便赶上第一班车。
I come here only to say good-bye to you. 我来仅仅是向你告别。

2作结果状语，表事先没有预料到的，要放在句子后面。
What have I said to make you angry.

3表原因
I'm glad to see you.

伴随状语