
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
On a blackboard, there are the numbers 1, 2, 3, 4, 5, and 6. In each move, João can replace two numbers \(a\) and \(b\) with \(a \cdot b + a + b\). Find all the possibilities for the last number on the blackboard.

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