Rough estimation. Reasoning + answer is ~1k tokens. API price for Chat GPT 5.5 is $30 per 1mil of output tokens, $5 per mil, for new input tokens and $0.50 for cached tokens. They allow 3k reasoning prompts per week.
Quick math 12000prompts x1000tokens=12mil tokens per month which will be 12x30= $360 add all long context costs at and you can double or triple that cost.
If you consider non reasoning prompting cost can be scaled to infinity since as far I'm aware subscription offers unlimited access for that. But they have anti abuse clause in the agreement, so I doubt you'll get to anywhere close to $14k cost