
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 domain of the function $f(x) = \sqrt{5-x} + \log(x+1)$ is set $A$ and the domain of the function $g(x) = \log(x^2 - 2x + a)$ is set $B$.

(I) When $a = -8$, find $A \cap B$;

(II) If $A \cap B' = \{x \mid -1 < x \leq 3\}$, find the value of $a$.

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