
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 integers starting from $100$ to $268$ in a $13 \times 13$ grid. He begins by placing $100$ in the middle square (seventh row and seventh column) and continues placing numbers one by one clockwise in a spiral pattern. Determine the sum of the greatest number and the least number that appear in the third row from the top.

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