
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 sets $M = \left\{\frac{b}{a}, 1\right\}$ and $N = \{a, 0\}$ exist, and a mapping $f: x \to x$ maps element $x$ in set $M$ to the set $N$ while remaining the same $x$, calculate the value of $a + b$.

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