
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 10 units and horizontally to the right by 5 units, and \( B \) is moved vertically downwards by 5 units and horizontally to the left by 5 units, what is the new midpoint \( M' \)? Calculate the distance between \( M \) and \( M' \).

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