
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
Let set A be the domain of the function $y = \ln(-x^2 - 2x + 8)$, set B be the range of the function $y = x + \frac{1}{x+1}$, and set C be the solution set of the inequality $(ax - \frac{1}{a})(x+4) \leq 0$.
(1) Determine $A \cap B$;
(2) If $C \subseteq \complement_{\mathbb{R}}A$, find the range of values for $a$.

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