
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 $A(x_1, y_1)$ and $B(x_2, y_2)$ is $M(x_m, y_m)$. If point $A$ is moved vertically upwards by 10 units and horizontally to the right by 5 units, and point $B$ is moved vertically downwards by 5 units and horizontally to the left by 15 units, then the new midpoint between the adjusted positions of $A$ and $B$ is $M'$. 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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