
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 the Cartesian plane, consider two points $A(a, b)$ and $B(c, d)$. Initially, the midpoint $M(m, n)$ is the average of coordinates $A$ and $B$. Suppose $A$ is shifted upwards by 10 units and rightwards by 5 units, while $B$ is shifted downwards by 5 units and leftwards by 15 units. Find the coordinates of the new midpoint, $M'$, and determine the distance between $M$ and $M'$.

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