
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 in a kingdom $\frac{1}{3}$ of the knights are green, and $\frac{1}{5}$ of the knights are magical, and the fraction of green knights who are magical is $3$ times the fraction of yellow knights who are magical, find the fraction of green knights who are magical.

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