
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]


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Real numbers \( a \) and \( b \) are chosen such that \( 2 < a < b \) ensuring that no triangle with positive area can have side lengths \( 2, a, \) and \( b \) or \( \frac{1}{b}, \frac{1}{a}, \) and \( 2 \). Determine the smallest value of \( b \) allowing these conditions.

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