
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 $\{a_n\}$ whose sum of the first $n$ terms is $s_n$, with $a_1=-\frac{2}{3}$, and satisfying $s_n+ \frac{1}{{s_n}}+2=a_n$ for $n\geqslant 2$, calculate $s_1$, $s_2$, $s_3$, $s_4$, and conjecture the expression for $s_n$.

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