
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
Sets  $A_0, A_1, \dots, A_{2023}$  satisfies the following conditions:


- $A_0 = \{ 3 \}$
- $A_n = \{ x + 2 \mid x \in A_{n - 1} \} \ \cup \{x(x+1) / 2 \mid x \in A_{n - 1} \}$  for each  $n = 1, 2, \dots, 2023$ .

Find  $|A_{2023}|$ .

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