
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

At a conference, there are several scientists, some of whom speak English, some French, and some German. The organizers noticed the following distribution:
- Among those who speak English, exactly \( \frac{1}{5} \) speak French, and exactly \( \frac{1}{3} \) speak German.
- Among those who speak French, exactly \( \frac{1}{8} \) speak English, and exactly \( \frac{1}{2} \) speak German.
- Among those who speak German, exactly \( \frac{1}{6} \) speak English.

What fraction of those who speak German also speak French?

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