
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
Given rows 101, 102, and 103 of Pascal's triangle, represented by sequences \((a_i)\), \((b_i)\), and \((c_i)\) respectively, compute
\[
\sum_{i = 0}^{101} \frac{b_i}{c_i} - \sum_{i = 0}^{100} \frac{a_i}{b_i}.
\]

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