
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
In the Cartesian coordinate plane, three sets of points are given: $A_{n}$, $B_{n}$, and $C_{n}$, where $A_{n}(n,a_{n})$, $B_{n}(n,b_{n})$, and $C_{n}(n-1,0)$. It is known that vector $\overrightarrow{A_{n}A_{n+1}}$ is collinear with vector $\overrightarrow{B_{n}C_{n}}$, and $b_{n+1}-b_{n}=6$, $a_{1}=b_{1}=0$. Find $a_{n}=$ _____ (express the answer in terms of $n$).

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