
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
Chicken eggs cost $0.50 each, duck eggs cost $0.60 each, and goose eggs cost $0.90 each. A man sold $x$ chicken eggs, $y$ duck eggs, and $z$ goose eggs and received $60. If $x$, $y$, $z$ are all positive numbers with $x + y + z = 100$ and two of the values $x$, $y$, $z$ are equal,

Find $x$.

Find $y$.

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