
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 \(\overline{a_{1} a_{2} \ldots a_{2009}}\) is a 2009-digit integer such that for each \(i=1,2, \ldots, 2007\), the 2-digit integer \(\overline{a_{i} a_{i+1}}\) contains 3 distinct prime factors. Find \(a_{2008}\). 

(Note: \(xyz \ldots\) denotes an integer whose digits are \(x, y, z, \ldots\))

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