
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 food factory produces a kind of chocolate candy with a cost of $24$ yuan per kilogram. There are two sales plans as follows:

- Plan 1: If sold directly to the factory's store in Hangzhou, the selling price is $32$ yuan per kilogram, but the store needs to pay a monthly fee of $2400$ yuan.
- Plan 2: If sold directly to a local supermarket, the factory price is $28$ yuan per kilogram.

If only one sales plan can be chosen each month, and each plan can sell all the products of that month, let the monthly sales volume of the factory be $x$ kilograms.

(1) As the factory manager, how should you choose the sales plan to maximize the monthly profit of the factory?

(2) After seeing the sales volume and profit relationship report for the first quarter sent by the accountant (as shown in the table below), the factory manager found discrepancies between the reported sales volume and the actual sales volume. Find the discrepancies and calculate the actual total sales volume for the first quarter.

|          | January | February | March |
|----------|---------|----------|-------|
| Sales (kg)| $550$   | $600$    | $1400$|
| Profit   | $2000$  | $2400$   | $5600$|

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