
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 a sequence $\left\{a_{n}\right\}$ with the sum of the first $n$ terms $S_{n}$ related to $a_{n}$ by the equation $S_{n}=-b a_{n}+1-\frac{1}{(1+b)^{n}}$, where $b$ is a constant independent of $n$ and $b \neq -1$:

(1) Find the expression for $a_{n}$ in terms of $b$ and $n$.

(2) When $b=3$, from which term does the sequence $\left\{a_{n}\right\}$ satisfy $S_{n}-a_{n}>\frac{1}{2}$?

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