
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 proposition $p$: "For all $x \in [1,2]$, $\frac{1}{2}x^2 - \ln(x-a) \geq 0$" and the proposition $q$: "There exists $x \in \mathbb{R}$, such that $x^2 + 2ax - 8 - 6a = 0$", if the proposition "$p \land q$" is true, then the range of the real number $a$ is ______.

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