
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
A three-digit (integer) number has a property that removing either the hundreds or the units digit results in a two-digit number that is 8 times the removed digit. What is the ratio of the two-digit number formed by the remaining digits to the single-digit number if the middle digit is removed?

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