
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
Let  $A$  be the number of  $12$ -digit words that can be formed by from the alphabet  $\{0,1,2,3,4,5,6\}$  if each pair of neighboring digits must differ by exactly  $1$ .  Find the remainder when  $A$  is divided by  $2008$ .

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