
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 function $f(x) = - \frac{1}{b}e^{ax}$ (where $a > 0, b > 0$), if the graph of this function has its tangent line at $x=0$ tangent to the circle $x^{2} + y^{2} = 1$, find the maximum value of $a+b$.

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