
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
For two positive numbers $m$ and $n$, both not equal to $1$, define: $m*n=\left\{{\begin{array}{l}{{{log}_m}n,m≥n}\\{{{log}_n}m,m＜n}\end{array}}\right.$. Let $a$, $b$, and $c$ be positive numbers less than $1$, and $ab=c$. Then the value of $\left(a*c\right)^{-1}+\left(b*c\right)^{-1}$ is ______.

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