
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

A fragment of a table, known as Leibniz's triangle, is shown below. Its properties are "analogous in the opposite sense" to those of Pascal's triangle. The boundary numbers of the triangle are the reciprocals of consecutive natural numbers. Each number inside the triangle equals the sum of the two numbers directly below it. Find a formula that relates the numbers from Pascal's triangle and Leibniz's triangle.

$$
\begin{aligned}
& \frac{1}{1} \\
& \frac{1}{2} \quad \frac{1}{2} \\
& \frac{1}{3} \quad \frac{1}{6} \quad \frac{1}{3} \\
& \begin{array}{llll}
\frac{1}{4} & \frac{1}{12} & \frac{1}{12} & \frac{1}{4}
\end{array} \\
& \begin{array}{lllll}
\frac{1}{5} & \frac{1}{20} & \frac{1}{30} & \frac{1}{20} & \frac{1}{5}
\end{array} \\
& \begin{array}{llllll}
\frac{1}{6} & \frac{1}{30} & \frac{1}{60} & \frac{1}{60} & \frac{1}{30} & \frac{1}{6}
\end{array}
\end{aligned}
$$

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