
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 $\left\{a_n\right\}$, if $a_{10}=0$, then the equation $a_{1}+a_{2}+\cdots +a_{n}=a_{1}+a_{2}+\cdots +a_{19-n}$ $(n < 19,n\in \mathbb{N})$ holds. By analogy, in the geometric sequence $\left\{b_n\right\}$, if $b_{9}=1$, then the equation                holds.

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