
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 $a$ and $b$ be real numbers, and let the sets be $M=\left\{\frac{b}{a}, 1\right\}$ and $N=\{a, 0\}$. The function $f: x \to 2x$ maps elements $x$ from set $M$ to elements $2x$ in set $N$. Find the value of $a+b$.

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