
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 an arithmetic sequence $\{a_n\}$, the sum of the first $n$ terms is denoted as $S_n (n\in \mathbb{N}_{*})$, and $a_n = 2n + \lambda$. If the sequence $\{S_n\}$ is increasing for $\{n | n \geqslant 5, n \in \mathbb{N}_{+}\}$, determine the range of real number $\lambda$.

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