
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 two pitchers, one with a capacity of 500 mL and the other with a capacity of 800 mL, each partly filled with orange juice. The smaller pitcher is $\frac{1}{4}$ full, while the larger pitcher is $\frac{1}{2}$ full. Calculate the fraction of the mixture in the large container when filled with water and the contents of both pitchers are combined.

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