
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 a sequence $\left\{a_{n}\right\}$ where $a_{1}=1$, $a_{2}=-13$, and $a_{n+2}-2a_{n+1}+a_{n}=2n-6$.
1. Let $b_{n}=a_{n+1}-a_{n}$, find the general formula for the sequence $\left\{b_{n}\right\}$.
2. Determine the value of $n$ for which $a_{n}$ is the smallest.

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