
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 $b_1,$ $b_2,$ $\dots,$ $b_{15}$ be positive real numbers such that $b_1 + b_2 + \dots + b_{15} = 1.$ Find the minimum value of \[\frac{1}{b_1} + \frac{1}{b_2} + \dots + \frac{1}{b_{15}}.\]

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