
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 real numbers $a$ and $b$ be chosen with $2 < a < b$ such that no triangle with positive area has side lengths $2, a,$ and $b$ or $\tfrac{1}{b}, \tfrac{1}{a},$ and $2$. What is the smallest possible value of $b$?

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