
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 \( A = \left\{ x \mid (a-1)x^{2} + 3x - 2 = 0 \right\} \), does there exist a real number \( a \) such that the set \( A \) has exactly two subsets? If such a real number \( a \) exists, find the value of \( a \) and the corresponding two subsets; if it does not exist, provide a reason.

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