
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
In the arithmetic sequence $\{a\_n\}$, if $a\_{10}=0$, then the equation $a\_1+a\_2+...+a\_n=a\_1+a\_2+...+a\_{19-n} (n < 19, n\in \mathbb{N}^*)$ holds. By analogy, in the geometric sequence $\{b\_n\}$, if $b\_9=1$, then \_\_\_\_\_\_.

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