
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
(12 points) Given that proposition p: "For all $x \in [1,2]$, $x^2 - \ln x - a \geq 0$" and proposition q: "There exists $x \in \mathbb{R}$, $x^2 + 2ax - 8 - 6a = 0$" are both true statements, find the range of the real number $a$.

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