
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 the smallest \( k \) among any three nonzero real numbers, can we choose two numbers \( a \) and \( b \) such that \( |a - b| \leq k \) or \( \left|\frac{1}{a} - \frac{1}{b}\right| \leq k \)?

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