
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
Write down a general formula for each of the following sequences:  
(1) The sequence of all positive even numbers $\{a_n\}$.  
(2) The sequence of all positive odd numbers $\{b_n\}$.  
(3) The sequence 1, 4, 9, 16, … .  
(4) The sequence -4, -1, 2, 5, …, 23.

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