
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 that Emily places 6 ounces of tea into a twelve-ounce cup and 6 ounces of honey into a second cup of the same size, and then adds 3 ounces of lemon juice to the second cup, then she pours half the tea from the first cup into the second, mixes thoroughly, and finally pours one third of the mixture in the second cup back into the first, calculate the fraction of the mixture in the first cup that is now lemon juice.

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