
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
After an earthquake in a certain area, according to information from the disaster relief command center, two severely affected areas, Area A and Area B, urgently need a large excavator. Area A needs 27 units, and Area B needs 25 units. Provinces A and B, upon learning of the situation, generously donated 28 units and 24 units of the same model excavator, respectively, and transported all of them to the disaster areas. If it costs 0.4 million yuan to transport one excavator from Province A to Area A, and 0.3 million yuan to Area B; from Province B to Area A, it costs 0.5 million yuan, and to Area B, it costs 0.2 million yuan. Let $x$ represent the number of excavators transported from Province A to Area A. Provinces A and B will transport all donated excavators to the disaster areas at a total cost of $y$ million yuan.

$(1)$ Fill in the table below with algebraic expressions involving $x$:

|          | Transported to Area A (units) | Transported to Area B (units) |
|----------|-------------------------------|-------------------------------|
| Province A | $x$                           | ______                        |
| Province B | ______                        | ______                        |

|          | Cost to transport to Area A (million yuan) | Cost to transport to Area B (million yuan) |
|----------|--------------------------------------------|--------------------------------------------|
| Province A | $0.4x$                                     | ______                                     |
| Province B | ______                                     | ______                                     |

$(2)$ Find the functional relationship between $y$ and $x$, and directly state the range of values for the independent variable $x$.

$(3)$ If the total cost does not exceed 16.2 million yuan, what are the possible transportation plans?

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