
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
Write in ascending order the multiples of 3 which, when 1 is added, are perfect squares, i.e., $3, 15, 24, 48, \ldots$ What is the multiple of 3 in the $2006^{\mathrm{th}}$ position?

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