
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 following statements:
1. $$4(-2)^{4} = \pm2$$;
2. For $y=x^{2}+1$, where $x \in [-1, 2]$, the range of $y$ is $[2, 5]$;
3. The graph of a power function never passes through the fourth quadrant;
4. The graph of the function $f(x) = a^{x+1} - 2$ ($a > 0$, $a \neq 1$) passes through the fixed point $(-1, -1)$;
5. If $\ln a < 1$, then the range of $a$ is $(-\infty, e)$.

The correct statement numbers are __________.

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