
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 $9'\times 12'$ needs to be moved from one corner to another inside a rectangular room. The shorter wall of the room is denoted by $W$ feet and the longer wall by $L$ feet. What is the smallest integer value for $W$, assuming $L \geq W$, such that the table can be relocated within the room without tilting or disassembling?

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