
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
Given the sequence ${a_n}$ where $a_1=2$ and $a_{n+1}=3a_n+2$, let $b_n=a_n+1$.

1. Find $b_1$, $b_2$, and $b_3$.
2. Determine if the sequence ${b_n}$ is a geometric sequence and explain your reasoning.
3. Find the general formula for the sequence ${a_n}$.

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