
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
(1) Find the solution set of the equation ${(\frac{x-1}{x})}^{2}-\frac{7}{2}(\frac{x-1}{x})+3=0$.  
(2) Find the solution set of the inequality in terms of $x$ when $a \lt 0$: $ax^{2}+\left(a-1\right)x-1 \lt 0$.

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