
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 $\{a\_n\}$ satisfying $a_{n+1} = a_{n} + 1$ for any $n ∈ ℕ^*$, and $a_{3} = 2$.
1. Find the general term formula for the sequence $\{a\_n\}$.
2. If $b_{n} = (\frac{1}{3})^{a_{n}} + n$, find the general term formula and the sum of the first $n$ terms for the sequence $\{b\_n\}$.

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