
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
Which of the following is the set of all perfect squares that can be written as sum of three odd composite numbers? $\textbf{a)}\ \{(2k + 1)^2 : k \geq  0\}$  $\textbf{b)}\ \{(4k + 3)^2 : k \geq  1\}$  $\textbf{c)}\ \{(2k + 1)^2 : k \geq  3\}$  $\textbf{d)}\ \{(4k + 1)^2 : k \geq 2\}$  $\textbf{e)}\ \text{None of above}$ 

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