
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 $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$, $a_1=1$, and $a_{n+1}=1-\frac{S_n}{2}$.

(1) Find the general formula for $\{a_n\}$.

(2) If $\{S_n + \lambda (n+\frac{1}{2^n})\}$ forms an arithmetic sequence, find the value of $\lambda$.

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