
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
If 48 lemons are required to make 64 gallons of lemonade, and if lemons and limes are used in different proportions to make their respective beverages, calculate how many lemons would be needed to make 10 gallons of lemonade. Assume that limes are used at a ratio of 1 lime per 2 gallons of limeade if it is known that 20 gallons of limeade is also to be made.

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