
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 \(0 < b_{1} < b_{2} < \ldots < b_{n}\). Then for any \(k\) less than \(n\),

$$
\frac{b_{1} + b_{2} + \ldots + b_{k}}{k} < \frac{b_{1} + b_{2} + \ldots + b_{n}}{n}
$$

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