
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
List, in increasing order, each multiple of 3 whose sum with 1 is a perfect square:

$$
3, 15, 24, 48, \ldots
$$

a) What is the next number that will appear in this sequence after 48?

b) What is the eighth number in this sequence?

c) What number will appear in the 2013th position of this sequence?

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