
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 \( f(x) = x^2 + ax + b \) where \( a, b \in \mathbb{R} \). Define \( A = \{x \mid f(x) = x, x \in \mathbb{R}\} \) and \( B = \{x \mid f(f(x)) = x, x \in \mathbb{R}\} \). If \( A = \{-1, 3\} \), then determine the set \( B \).

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