
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 ${S_n}$, it satisfies the conditions ${S_{2018}} > 0, {S_{2019}} < 0$. For any positive integer $n$, $|{a_n}| \geq |{a_k}|$. Find the value of $k$.

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