
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
Given the original cost of drink A is 5 yuan for every 500 grams, and the original cost of drink B is 4 yuan for every 500 grams, and after a 10% increase in the cost of A and a 10% decrease in the cost of B, the cost of the new beverage remains unchanged, determine the ratio of the weights of A to B.

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