
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
If $(x+2)^n = x^n + \ldots + ax^3 + bx^2 + cx + 2^n$ (where $n \in \mathbb{N}$, and $n \geq 3$), and the ratio of $a$ to $b$ is $3:2$, then $n = \_\_\_\_\_\_$.

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