
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 proposition p: The function $f(x) = \lg(x^2 + ax - a - 1)$ is monotonically increasing in the interval $[2, +\infty)$, and proposition q: The function $g(x) = x^3 - ax^2 + 3ax + 1$ has both a maximum and a minimum value in the interval $(-\infty, +\infty)$, find the range of real numbers $a$ for which exactly one of the propositions p and q is true.

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