
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
Let  $n$  be a nonnegative integer less than  $2023$  such that  $2n^2 + 3n$  is a perfect square. What is the sum of all possible  $n$ ?

*Proposed by Giacomo Rizzo*

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