
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
How many sequences  $ a_1,a_2,...,a{}_2{}_0{}_0{}_8$  are there such that each of the numbers  $ 1,2,...,2008$  occurs once in the sequence, and  $ i \in (a_1,a_2,...,a_i)$  for each  $ i$  such that  $ 2\le i \le2008$ ?

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