
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
Let the length she weaves on the first day be $x$. On the second day, she weaves $x + y$ feet, where $y$ is the daily increase. On the fifth day, she weaves $x + 4y$ feet, and on the eighth day, she weaves $x + 7y$ feet. Given that she weaves $x + 3y + x + 4y + x + 7y = 28$ feet in seven days and $x + 4y + x + 7y = 15$ feet, determine the length she weaves on the tenth day.

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