
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 $a$ and $b$ are two distinct real numbers, and the sets $A=\{a^2-4a, -1\},$ $B=\{b^2-4b+1, -2\}$. If the mapping $f: x \rightarrow x$ represents mapping the element $x$ in set $A$ to set $B$ while still being $x$, determine the value of $a+b$.

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