
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 $f(x) = \lg(x^2 + ax - a - 1)$, determine the correct proposition among the following:

1. The function $f(x)$ has a minimum value.
2. When $a = 0$, the range of the function $f(x)$ is $R$.
3. If the function $f(x)$ is monotonically decreasing on the interval $(-\infty, 2]$, then the range of the real number $a$ is $a \leqslant -4$.

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