
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
In the "Zhang Qiujian's Mathematical Manual," an important mathematical work during the Southern and Northern Dynasties of China, arithmetic progressions are systematically introduced. Similar results only appeared in India more than three hundred years later. The book contains the following problem: A woman is skilled at weaving. She weaves faster each day than the previous one, with the same amount of increase in speed each day. It is known that on the first day she wove 5 chi (a unit of length), and a total of 390 chi in a month (considering a month to be 30 days). How much does her weaving increase by each day?

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