
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
In a kingdom, there are knights of two colors: red and blue. $\frac{1}{3}$ of them are red, and the rest are blue. Of all the knights, $\frac{1}{5}$ are magical. If the fraction of blue knights who are magical is $\frac{2}{3}$ times the fraction of the red knights who are magical, calculate the fraction of the red knights who are magical.

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