
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 integers from 1 to 20 are written on the board. You can erase any two numbers, $a$ and $b$, and write the number $a+b-1$ in their place. What number will be written on the board after 19 operations? And what if instead of writing $a+b-1$, you wrote $a+b+a b$?

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