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"Jumping to a conclusion" is not knowing all the facts and forming a conclusion. Drawing a conclusion is learning all the facts to make a conclusion if it is correct or not.
The conclusion may only apply to the patterns that you observe and so you simply use your observational skills. There is no requirement for the conclusion to be a generalisation. If the conclusion is a generalisation based on the observed patterns then you will have used induction.
Proof
The solution is when the problem is solved. It can be anywhere - many stories have more than one problem in the plot. The conclusion is when it is the end of the story and everything draws to a close.
The conclusion or deduction.