
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 function $f(x)=\log_2 g(x) + (k-1)x$.

    (1) If $g(\log_2 x) = x + 1$ and $f(x)$ is an even function, find the value of the real number $k$;

    (2) When $k=1$, $g(x) = ax^2 + (a+1)x + a$, and the range of the function $f(x)$ is $\mathbb{R}$, find the range of values for the real number $a$.

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