
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
There are 128 ones written on the board. In one move, you can replace a pair of numbers $a$ and $b$ with the number $ab+1$. Let $A$ be the maximum number that can result on the board after 127 such operations. What is the last digit of this number?

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