
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 that point P($n, a_n$) ($n \in \mathbb{N}^*$) lies on the graph of the function $f(x) = \frac{2x+4}{x}$, and the sequence $\{b_n\}$ satisfies $b_n = a_n + \lambda n$. If the sequence $\{b_n\}$ is increasing, then the range of values for the positive real number $\lambda$ is ______.

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