
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
1. The transformation  $ n \to 2n \minus{} 1$  or  $ n \to 3n \minus{} 1$ , where  $ n$  is a positive integer, is called the 'change' of  $ n$ . Numbers  $ a$  and  $ b$  are called 'similar', if there exists such positive integer, that can be got by finite number of 'changes' from both  $ a$  and  $ b$ . Find all positive integers 'similar' to  $ 2005$  and less than  $ 2005$ .

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