
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
Define "geometric sequence": In a sequence, if the product of each term and its next term is the same constant, then this sequence is called a geometric sequence, and this constant is called the common product of the sequence. It is known that the sequence $\{a_n\}$ is a geometric sequence, and $a_1 = 3$, the common product is $15$, then $a_{21} = \boxed{3}$.

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