
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 with \(2 < a < b\) such that no triangle with positive area has side lengths \(2, a,\) and \(b\) or \(\frac{1}{b}, \frac{1}{a},\) and \(2\). What is the smallest possible value of \(b\)?

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