
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 the general formulas for sequences $\{a_n\}$ and $\{b_n\}$ are $a_n = an + 2$ and $b_n = bn + 1$ (where $a$ and $b$ are constants), and $a > b$, determine the number of terms that have both the same index and value in the two sequences.

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