
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 company needs to transport two types of products, $A$ and $B$, with the following volumes and masses per unit as shown in the table:

|          | Volume $(m^{3}/$unit) | Mass (tons$/$unit) |
|----------|-----------------------|--------------------|
| $A$ type | $0.8$                 | $0.5$              |
| $B$ type | $2$                   | $1$                |

1. Given a batch of products containing both $A$ and $B$ types with a total volume of $20m^{3}$ and a total mass of $10.5$ tons, find the number of units for each type of product.

2. A logistics company has trucks with a rated load of $3.5$ tons and a capacity of $6m^{3}$. The company offers two payment options:
   - Charging per truck: $600$ yuan per truck to transport goods to the destination.
   - Charging per ton: $200$ yuan per ton to transport goods to the destination.
   
   Determine how the company should choose to transport the products from part (1) in one or multiple shipments to minimize the shipping cost, and calculate the cost under the chosen method.

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