
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 that $\{a_{n}\}$ is an arithmetic sequence, $b_{n}=\sin (a_{n})$, and there exists a positive integer $t$ such that for any positive integer $n$, $b_{n+t}=b_{n}$. If the set $S=\{x|x=b_{n}$, $n\in N^{*}\}$ contains only $4$ elements, determine the possible values of $t$.

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