
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 the Cartesian plane, the midpoint between two points $A(a, b)$ and $B(c, d)$ is $M(m, n)$. If $A$ is moved vertically upwards by 12 units and horizontally to the right by 5 units, and $B$ is moved vertically downwards by 6 units and horizontally to the left by 15 units, calculate the new midpoint $M'$ between $A$ and $B$ after their movement, and determine the distance between $M$ and $M'$.

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