
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
Let set \( A = \left\{ x \mid 2x - x^2 \leq x \right\} \), set \( B = \left\{ x \mid \frac{x}{1-x} \leqslant \frac{x}{1-x} \right\} \), and set \( C = \left\{ x \mid ax^2 + x + b < 0 \right\} \). Given that \( (A \cup B) \cap C = \varnothing \) and \( (A \cup B) \cup C = \mathbb{R} \), find the values of \( a \) and \( b \).

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