
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
Three numbers are given. If each of them is increased by 1, their product also increases by 1. If all the original numbers are increased by 2, their product also increases by 2. Find these numbers.

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