
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 the function $y=a^x$ (where $a>0$ and $a \neq 1$) has an inverse function $y=f^{-1}(x)$, if $f^{-1}(m)+f^{-1}(n)=0$, find the minimum value of $m+n$.

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