
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 seven glasses of water: the first glass is half full, the second is one-third full, the third is one-quarter full, the fourth is one-fifth full, the fifth is one-eighth full, the sixth is one-ninth full, and the seventh is one-tenth full. You are allowed to either pour all the water from one glass into another or pour water from one glass into another until it is full. After several pourings, can any glass be filled to a) one-twelfth; b) one-sixth?



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