
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 $\{a_n\}$ satisfying: $a_3 =-13$, $a_n=a_{n-1}+4$ (where $n > 1$ and $n \in \mathbb{N}$).
(1) Find $a_1$, $a_2$, and the general term $a_n$;
(2) Let $S_n$ be the sum of the first $n$ terms of the sequence $\{a_n\}$. Which term of the sequence $S_1$, $S_2$, $S_3$, … is the smallest?

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