
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
Let two glasses, numbered  $1$  and  $2$ , contain an equal quantity of liquid, milk in glass  $1$  and coffee in glass  $2$ . One does the following: Take one spoon of mixture from glass  $1$  and pour it into glass  $2$ , and then take the same spoon of the new mixture from glass  $2$  and pour it back into the first glass. What happens after this operation is repeated  $n$  times, and what as  $n$  tends to infinity?

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