
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
Three pitchers with capacities of $500$ mL, $700$ mL, and $800$ mL have orange juice. The first pitcher is $1/5$ full, the second is $3/7$ full, and the third is $1/4$ full. After topping each pitcher off with water, all the contents are poured into a large container. What fraction of the mixture in the large container is orange juice?

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