
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
The numbers from  $1$  to  $100$  are arranged in a  $10\times 10$  table so that any two adjacent numbers have sum no larger than  $S$ . Find the least value of  $S$  for which this is possible.
*D. Hramtsov*

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