
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 $a_1 + a_2 + \ldots + a_n = a_1 + a_2 + \ldots + a_{19-n}$ holds (where $n < 19$ and $n \in \mathbb{N}^*$). Drawing an analogy from the above property, in the geometric sequence $\{b_n\}$, if $b_9 = 1$, then the equation _______ holds.

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