
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 of real numbers $\mathrm{R}$, the function $f(x) = x^2 + a x + b$ where $a, b \in \mathrm{R}$, and the sets $A = \{x \mid x = f(x), x \in \mathrm{R}\}$ and $B = \{x \mid x = f(f(x)), x \in \mathrm{R}\}$, find the following:

1. When $A = \{-1, 3\}$, what is $B$?
2. Describe the relationship between $A$ and $B$.

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