
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
Real numbers $a$ and $b$ are chosen such that $k < a < b$ with $k>1$. It must hold that no triangle with side lengths $k, a,$ and $b$, or $\frac{1}{b}, \frac{1}{a},$ and $\frac{1}{k}$ forms a non-degenerate triangle. What is the smallest possible value of $b$?

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