
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
For the arithmetic sequence $\{a_n\}$, there is a true proposition: "If $\{a_n\}$ is an arithmetic sequence, and $a_1=0$, $s$ and $t$ are distinct positive integers, then $(s-1)a_t-(t-1)a_s=0$." Analogously, for the geometric sequence $\{b_n\}$, there is a true proposition: If $\{b_n\}$ is a geometric sequence, and $b_1=$ ______, $s$ and $t$ are distinct positive integers, then ______.

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