
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
Mr. Zhang arranges all integers from $1$ to $289$ into a $17 \times 17$ grid. He places $1$ in the middle square (ninth row and ninth column) and places other numbers one by one counterclockwise, beginning from the center. Determine the sum of the greatest and least numbers that appear in the third row from the top.

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