
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
Katka cut a square scarf depicted in the picture along its diagonal and obtained two triangular scarves. Determine what fraction of each new scarf is white, black, and gray. On the original scarf, black was $\frac{1}{6}$ and gray was $\frac{1}{3}$ of its area.

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