
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
In a Cartesian plane, there are two points $A(a, b)$ and $B(c, d)$. The midpoint between these points is $M(x, y)$. If point $A$ is moved horizontally to the left by 5 units and vertically downward by 3 units, and point $B$ is moved horizontally to the right by 4 units and vertically upward by 6 units, determine the new midpoint, $M'$, and find the distance between the midpoints $M$ and $M'$.

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