
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 that $a$ and $b$ are two different real numbers, the sets $M={a^{2}-4a,-1}$ and $N={b^{2}-4b+1,-2}$, and the function $f: x→x$ maps the elements in set $M$ to the elements in set $N$ such that they remain $x$. Find the value of $a+b$.

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