这句句子是主从复合句：The hunt for the puma began in a small village是主句，where引导的定语从句修饰village，从句里picking blackberries 是现在分词短语作定语修饰从句中的主语woman。
主句中The hunt for the puma 是主语， began 是谓语 in a small village是地点状语；从句中a woman picking blackberries是主语， saw是谓语，a large cat是宾语，only five yards away from her是地点状语。
The hunt是主语，began是谓语，过去时的形式，in a small village是地点状语，这会还不是状语从句呢啊。后面where引导才是一个地点状语从句。picking blackberries 只是一个定语，不能称为从句。能称上从句的必须是又主谓宾或者引导词来补充主谓宾中缺少的成分。希望回答正确。
The hunt for the puma began in a small village where a woman picking blackberries saw a large cat only five yards away from her.特别是picking 那个地方，谢谢了 
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