
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 set $P = \{x \mid x \leq 3\}$, the domain of the function $f(x) = \log_{2}(ax^{2} - 2x + 2)$ is $Q$.

(1) If $P \cap Q = (\ , )$ and $P \cup Q = (-2, 3]$, then the value of the real number $a$ is $\boxed{\text{fill in the blank}}$;  
(2) If $P \cap Q = \emptyset$, then the range of values for the real number $a$ is $\boxed{\text{fill in the blank}}$.

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