
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 an arithmetic sequence $\{a_n\}$, if $a_8 = 0$, then the equation $a_1 + a_2 + a_3 + \ldots + a_n = a_1 + a_2 + a_3 + \ldots + a_{15-n}$ holds for $n < 15, n \in \mathbb{N}^*$. By analogy with this property, in a geometric sequence $\{b_n\}$, if $b_7 = 1$, then the equation ____________ holds.

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