
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  $\overline{a_1a_2...a_{2009}}$  is a  $2009$ -digit integer such that for each  $i = 1,2,...,2007$ , the  $2$ -digit integer  $\overline{a_ia_{i+1}}$  contains  $3$  distinct prime factors. Find  $a_{2008}$  
(Note:  $\overline{xyz...}$  denotes an integer whose digits are  $x, y,z,...$ .)

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