
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 functions $g(x)=x^{2}+(a-1)x+a-2a^{2}$ and $h(x)=(x-1)^{2}$, let set $A$ be the solution set of the inequality $g(x) > 0$, and set $B$ be the solution set of the inequality $h(x) < 1$.
(1) If set $A \cap B \neq \emptyset$, find the range of real number $a$.
(2) Given $\log _{x}[f(x)]-\log _{x}[g(x)]=1$ and set $C$ as the solution set of the inequality $f(x) > 0$, if set $C \cap B \neq \emptyset$, find the range of real number $a$.

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