
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 coordinate system, consider two points $A(a,b)$ and $B(c,d)$. The midpoint between these points is $M(m,n)$. If point $A$ is moved vertically upwards by 6 units and horizontally to the left by 3 units, and point $B$ is moved vertically downwards by 3 units and horizontally to the right by 5 units, determine the new midpoint $M'$ between these modified positions of $A$ and $B$. What is the distance between the original midpoint $M$ and the new midpoint $M'$?

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