
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
Each cell of an infinite table (infinite in all directions) is colored with one of  $n$  given colors. All six cells of any  $2\times 3$  (or  $3 \times 2$ ) rectangle have different colors. Find the smallest possible value of  $n$ .

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