
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
For every integer  $ a>1$  an infinite list of integers is constructed  $ L(a)$ , as follows:

[list]  $ a$  is the first number in the list  $ L(a)$ .[/list]
[list] Given a number  $ b$  in  $ L(a)$ , the next number in the list is  $ b\plus{}c$ , where  $ c$  is the largest integer that divides  $ b$  and is smaller than  $ b$ .[/list]
Find all the integers  $ a>1$  such that  $ 2002$  is in the list  $ L(a)$ .

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