
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 function $f(x)=\lg(a-ax-x^2)$.
(Ⅰ) If the function $f(x)$ exists, find the range of values for $a$.
(Ⅱ) If $f(x)$ is defined for $x \in (2, 3)$, find the range of values for $a$.
(Ⅲ) If the solution set for $f(x) > 0$ is $(2, 3)$, find the value of $a$.

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