
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 a sequence, if for all $n \in \mathbb{N}^0$, we have $a_na_{n+1}a_{n+2} = k$ (where $k$ is a constant), then this sequence is called a geometric sequence, and $k$ is called the common product. Given that the sequence $a_n$ is a geometric sequence, and $a_1 = 1$, $a_2 = 2$, with a common product of 8, find the sum $a_1 + a_2 + a_3 + \ldots + a_{12}$.

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