
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 rectangular table with dimensions 9' by 12' is placed in the corner of a square room. The owners wish to reposition the table to the opposite corner without tilting or dismantling it. Find the smallest integer value of S, the side length of the room, that allows for the repositioning of the table.

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