
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
The teacher gave Jia Jia, Fang Fang, and Ming Ming a number each and then asked them to pick 3 cards with numbers written on them. Jia Jia picked 3, 6, and 7; Fang Fang picked 4, 5, and 6; and Ming Ming picked 4, 5, and 8. The teacher then instructed them to multiply any two numbers from their cards and add the number initially given by the teacher. If the numbers given by the teacher to each of them were 234, 235, and 236, and their calculations were correct, what different numbers could they possibly calculate?

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