
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 the first four terms of the sequences that satisfy the conditions, and deduce the general formula for each sequence:  
(1) $a_1=0$, $a_{n+1}=a_n+(2n-1)$ ($n\in\mathbb{N}^*$);  
(2) $a_1=3$, $a_{n+1}=3a_n$ ($n\in\mathbb{N}^*$).

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