
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 $\overrightarrow{a}=(4,-2,-4)$ and $\overrightarrow{b}=(6,-3,2)$. Find:  
$(1)$ $\overrightarrow{a} \cdot \overrightarrow{b}$;  
$(2)$ $|\overrightarrow{a}|$;  
$(3)$ $|\overrightarrow{b}|$;  
$(4)$ $(2\overrightarrow{a}+3\overrightarrow{b})\cdot(\overrightarrow{a}-2\overrightarrow{b})$.

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