
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
Let \( f(x) = \lg \left[\frac{1}{n}\left(1 + 2^x + \cdots + (n-1)^x + n^x a\right)\right] \), where \( a \in \mathbb{R}, n \in \mathbb{N} \) and \( n \geqslant 2 \). If \( f(x) \) is meaningful when \( x \in (-\infty, 1] \), find the range of values for \( a \).

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