
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
Let the geometric sequence $\{a_n\}$ consist of positive terms, and let $a_1+a_2+\ldots+a_6=1$, $\frac{1}{a_1}+\frac{1}{a_2}+\ldots+\frac{1}{a_6}=10$. Calculate the product $a_1a_2\ldots a_6$.

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