
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
On March 12, a tractor-driving couple working at a machine station made a work offer for April 4, stating that over the next 20 working days, the husband would increase his daily performance by $1\%$ of the previous day's performance, and the wife would increase her daily performance by $0.5\%$ of her own previous day's performance each day. On April 4, it was found that the couple had an average daily performance of $240\%$ together over the last 20 working days. How much did the husband and wife each perform in percentage on the first day, given that the wife's performance on the twentieth day was $101.2\%$?

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