
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 certain brand of shampoo comes in two sizes: the large bottle weighs 450g and is priced at 36 yuan, while the small bottle weighs 150g and is priced at 12.5 yuan. The simplest integer ratio of the prices of the large and small bottles of shampoo is ____, and it is more cost-effective to buy the ____ bottle.

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