
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 $\{a\_n\}$ satisfies $a\_1=1$, and the points $(a\_n, 2a_{n+1})(n∈N^*)$ are on the line $x-\frac{1}{2}y+1=0$. If for any $n∈N^*$, $$\frac{1}{n+a\_1} + \frac{1}{n+a\_2} + \frac{1}{n+a\_3} + ... + \frac{1}{n+a\_n} ≥ λ$$ always holds, then the range of the real number $λ$ is $\_\_\_\_\_\_\_\_\_\_\_$.

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