
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 $\{a_n\}$, where $$a_{n}+1=- \frac {1}{2}a_{n-1}- \frac {1}{2}$$ for $n\geq2$ and $n\in\mathbb{N}^*$, and $a_1=1$. Let $S_n$ denote the sum of the first $n$ terms of the sequence $\{a_n\}$. If $3λ•(S_n+n)\leq4$ holds true for any $n\in\mathbb{N}^*$, find the maximum value of the real number $λ$.

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