
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 $f(x) = a^x - 1$ ($a > 0$, and $a \neq 1$), when $x \in (0, +\infty)$, $f(x) > 0$, and the graph of the function $g(x) = f(x+1) - 4$ does not pass through the second quadrant, determine the range of values for $a$.

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