
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
Given Mrs. Wang creates a magic square by placing all integers from $1$ to $121$ into an $11 \times 11$ grid, she starts by placing the number $1$ in the bottom square of the central column (sixth row and sixth column) and then proceeds counterclockwise in a spiral upwards. What is the sum of the greatest and the least number that appear in the middle row from the top?

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