
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 certain supermarket had a clearance sale on several snacks on the Lantern Festival. It is known that the cost prices of chocolate, potato chips, and melon seeds are $12$ yuan per bag, $8$ yuan per bag, and $6$ yuan per bag, respectively. The ratio of the discounted selling prices is $10:6:5$, and the ratio of the sales volumes of the three products during the day is $1:2:2$. After 6 p.m., the supermarket had a big promotion where each product participated in a "buy 4 get 1 free" activity (meaning that every 5 bags bundled together were sold for the price of 4 bags). By the end of the business day, each product had sold half of its daytime sales volume, and the total sales volume for the day exceeded 250 bags but was less than 350 bags (the sales volume of products is an integer). It is given that the sales revenue for potato chips that day was 1344 yuan. Then the profit for the whole day is ____ yuan.

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