
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 \( A = \{ x \mid x^2 - 1 = 0 \} \) and \( B = \{ y \mid y^2 - 2ay + b = 0, y \in \mathbb{R} \} \), if \( B \subseteq A \) and \( B \neq \varnothing \), find the real values of \( a \) and \( b \).

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