
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
Ilya has a one-liter bottle filled with freshly squeezed orange juice and a 19-liter empty jug. Ilya pours half of the bottle's contents into the jug, then refills the bottle with half a liter of water and mixes everything thoroughly. He repeats this operation a total of 10 times. Afterward, he pours all that is left in the bottle into the jug. What is the proportion of orange juice in the resulting drink in the jug? If necessary, round the answer to the nearest 0.01.

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