
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
A man bought exactly 100 eggs for eight shillings and fourpence. The eggs he bought were of three different qualities: new-laid eggs at fivepence each, fresh eggs at one penny each, and eggs at a halfpenny each. He brought away the same number of eggs of two of the three qualities. Determine how many eggs he bought at each price.

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