
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 a positive integer $n$, let
\[ a_n = \sum_{k = 0}^n \frac{1}{\binom{n+1}{k}} \quad \text{and} \quad b_n = \sum_{k = 0}^n \frac{k}{\binom{n+1}{k}}. \]
Simplify $\frac{a_n}{b_n}$.

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