
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
When $(a-2b)^n, n \ge 2, ab \ne 0$, is expanded by the binomial theorem, it is found that when $a = 3b$, where $b$ is a positive integer, the sum of the second and third terms is zero. Determine the value of $n$.

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