
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
Last year, the electricity price in a certain city was 0.80 yuan per kilowatt-hour, with an annual electricity consumption of $a$ kilowatt-hours. This year, it is planned to reduce the electricity price to between 0.55 yuan and 0.75 yuan per kilowatt-hour, while residential users hope for an electricity price of 0.40 yuan per kilowatt-hour (the city's cost price for electricity is 0.30 yuan per kilowatt-hour). It has been calculated that after reducing the electricity price, the increase in electricity consumption in the city is inversely proportional to the difference between the actual electricity price and the user's expected price, with a proportionality constant of $0.2a$. The question is, what is the lowest electricity price that can ensure the revenue of the power department increases by at least 20% compared to last year?

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