
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 $(a_1+a_2+...+a_n)=(a_1+a_2+...+a_{19-n})$ holds true, where $n<19,n∈\mathbb{N}_+$. By analogy, in the geometric sequence $\{b_n\}$, if $b_9=1$, then the corresponding equation is:

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