
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
Residents in a certain area use electricity with a tiered pricing system, as follows: for each household, if the monthly electricity usage does not exceed $120$ kWh, the price is $0.6$ yuan per kWh; for usage exceeding $120$ kWh but not exceeding $300$ kWh, the price is $0.8$ yuan per kWh; for usage exceeding $300$ kWh but not exceeding $500$ kWh, the price is $1$ yuan per kWh; for usage exceeding $500$ kWh, the price is $1.2$ yuan per kWh. In a certain month, households $A$ and $B$ together paid a total of $y$ yuan for electricity. It is known that the electricity usage of households $A$ and $B$ in that month were $5x$ kWh and $2x$ kWh, respectively.
- $(1)$ Find the functional relationship of $y$ with respect to $x$.
- $(2)$ If households $A$ and $B$ together paid a total of $486$ yuan for electricity in that month, find the electricity usage of households $A$ and $B$.

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