
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 each multiple of 3 whose sum with the number 1 is a perfect square:

$$
3; \quad 15; \quad 24; 48; \quad \ldots
$$

What is the multiple in the $2006^{\text{th}}$ position?

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