
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
For the sequence $\{a_n\}$, where $n \in \mathbb{N}^+$, it satisfies $a_{n+1} = a_n + 1$, with $a_3 = 2$.
(1) Find the general term formula for the sequence $\{a_n\}$;
(2) Let $b_n = \left( \frac{1}{3} \right)^{a_n} + n$, find the general term formula for $\{b_n\}$ and the sum of the first $n$ terms.

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