
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 an arithmetic sequence ${a_n}$ with the sum of its first $n$ terms denoted as $S_n$, where $a_1 > 0$ and $n \in \mathbb{N}^*$. If $S_{12} > 0$ and $S_{13} < 0$, find the smallest term in the sequence $\{|a_n|\}$.

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