
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 points $A(-2,4)$, $B(3,-1)$, $C(m,-4)$, where $m\in \mathbb{R}$. <br/>$(1)$ When $m=-3$, find the cosine value of the angle between vectors $\overrightarrow{AB}$ and $\overrightarrow{BC}$; <br/>$(2)$ If points $A$, $B$, $C$ form a right-angled triangle with $A$ as the right angle vertex, find the value of $m$.

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