
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
Definition: Given two numbers $a$ and $b$, a new number $c$ is generated according to the rule $c=ab+a+b$. If a number $c$ can be obtained in this way, it is called a "new number". Starting with the numbers 1 and 4,  
① The largest new number $c^*$ obtained after operating according to the above rule three times is 49;  
② 2008 is not a new number;  
③ $c+1$ is always divisible by 2;  
④ $c+1$ is always divisible by 10;  
⑤ 499 cannot be a new number.  
Among these statements, the correct ones are.

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