
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
Suppose rows \( n \) and \( n+1 \) of Pascal's triangle have sequences \((a_i)\) and \((b_i)\) respectively, with elements ranging from \( i = 0 \) to \( n \). Compute the value of:
\[
\sum_{i = 0}^{n} i \cdot \frac{a_i}{b_i}
\]
when \( n = 2023 \).

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