
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
If $\{a_{n}\}$ is an arithmetic sequence, with the first term $a_{1} \gt 0$, $a_{2022}+a_{2023} \gt 0$, and $a_{2022}\cdot a_{2023} \lt 0$, then the smallest natural number $n$ for which the sum of the first $n$ terms $S_{n} \lt 0$ is ____.

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