
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 $(a_i), (b_i), (c_i)$ represent the sequence, from left to right, of elements in the 3001st, 3002nd, and 3003rd rows, respectively, of Pascal's triangle. The leftmost elements occur at $i = 0.$ Compute 
\[\sum_{i = 0}^{3002} \frac{b_i}{c_i} - \sum_{i = 0}^{3001} \frac{a_i}{b_i}.\]

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