
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 function \( f(x)=\frac{1}{2^{-1}} \) and the sequence \( \{a_{n}\} \) with the sum of the first \( n \) terms \( S_{n}=6 - 2a_{n} + f(n-1) \), find the general term formula for the sequence \( \{a_{n}\} \).

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