
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 that the right-angle vertex of a right-angled triangle is $C(-2,3)$, and the equation of the line containing the hypotenuse $AB$ is $4x-3y-7=0$, the slope of the line containing the median on the hypotenuse is $-\dfrac{4}{3}$. Find the coordinates of points $A$ and $B$.

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