
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
On a Cartesian plane, consider two points $A(a,b)$ and $B(c,d)$ with the midpoint $M(m,n)$. Suppose $A$ is translated 6 units upwards and 4 units to the right, while $B$ is translated 4 units downwards and 5 units to the left. Determine the distance between the original midpoint $M$ and the new midpoint $M'$ after these transformations.

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