
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
Initially, the number 10 is written on the board. In each subsequent move, you can either:
(i) erase the number 1 and replace it with a 10, or 
(ii) erase the number 10 and replace it with a 1 and a 25, or 
(iii) erase a 25 and replace it with two 10. 
After some time, you notice that there are exactly one hundred copies of 1 on the board. What is the least possible sum of all the numbers on the board at that moment?

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