
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
A square with a perimeter of 24 is inscribed in a square with a perimeter of 32. The inner square is rotated such that one of its vertices lies on the midpoint of one side of the outer square. What is the greatest distance between a vertex of the inner square and a vertex of the outer square?
A) 5
B) 7
C) 5√2
D) 7√2

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