$[40$ marks$]$ Manually train a decision tree based on the following dataset.

a$)$ Please show the detailed process of selecting an attribute to split the instance set at every node. Gini index should be used to measure the impurity $(30$ marks$).$

b$)$ Draw the final decision tree $(5$ marks$).$

c$)$ Classify the test instance rainy, $x2=$ hot, $x3=$ high, $x4=$ false