
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
Suppose there are  $n$  boxes in a row and place  $n$  balls in them one in each. The balls are colored red, blue or green. In how many ways can we place the balls subject to the condition that any box  $B$  has at least one adjacent box having a ball of the same color as the ball in  $B$ ? [Assume that balls in each color are available abundantly.]

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