
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 a bowl containing 320 grams of pure white sugar, mixture Y is formed by removing \( x \) grams of white sugar and adding \( x \) grams of brown sugar. The ratio of white to brown sugar in mixture Y is \( w:b \). Then mixture Z is formed by removing \( x \) grams of mixture Y and adding \( x \) grams of brown sugar, resulting in a ratio of white to brown sugar of \( 49:15 \) in mixture Z, where \( x+w+b \) is to be determined.

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