
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
To encourage residents to save electricity, a certain city has implemented a monthly tiered electricity pricing system as follows:

| Tier | Monthly Electricity Usage per Household (kWh) | Electricity Price (元/kWh) |
|------|-----------------------------------------------|-----------------------------|
| 1    | Less than or equal to 200                      | $0.5                        |
| 2    | Greater than 200 and less than or equal to 450 | $0.7                        |
| 3    | Greater than 450                               | $1                          |

$(1)$ If a household uses 300 kWh of electricity in July, the amount of electricity fee they need to pay is ______ yuan.  
$(2)$ A household used a total of 500 kWh of electricity in May and June, and paid 290 yuan for electricity. It is known that the electricity usage in June was greater than in May, and the electricity usage in both May and June was less than 450 kWh. Find out how much electricity the household used in May and June, respectively.

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