
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfy: $|\overrightarrow{a}|=2$, $|\overrightarrow{b}|=4$  
$(1)$ If $(\overrightarrow{a}-\overrightarrow{b})\cdot\overrightarrow{b}=-20$, find the angle between vector $\overrightarrow{a}$ and $\overrightarrow{b}$ and the magnitude of $|3\overrightarrow{a}+\overrightarrow{b}|$  
$(2)$ In rectangle $ABCD$, the midpoint of $CD$ is $E$, the midpoint of $BC$ is $F$, let $\overrightarrow{AB}=\overrightarrow{a}$, $\overrightarrow{AD}=\overrightarrow{b}$, express $\overrightarrow{AE}$ and $\overrightarrow{AF}$ using vectors $\overrightarrow{a}$, $\overrightarrow{b}$, and find the value of $\overrightarrow{AE}\cdot\overrightarrow{AF}$.

Present the answer in LaTex format: \boxed{Your answer}
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