
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
An $9'\times 12'$ table sits in the corner of a square room, as shown in the initial diagram. The owners desire to rotate the table $90^\circ$. What is the smallest integer value of $S$ for the side length of the room in feet, in which the table can be positioned as desired without tilting it or taking it apart?
A) 13
B) 14
C) 15
D) 16
E) 17

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