
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 area was ¥0.8 per unit, and the annual electricity consumption was 100 million kWh. This year, it is planned to adjust the electricity price to between ¥0.55 and ¥0.75. It has been calculated that if the electricity price is adjusted to ¥$x$, then the increase in electricity consumption this year, $y$ (in 100 million kWh), is inversely proportional to $(x-0.4)$. Furthermore, when $x=0.65$, $y=0.8$.

    (1) Find the functional relationship between $y$ and $x$;

    (2) If the cost price of electricity per kWh is ¥0.3, what should the electricity price be adjusted to so that the revenue of the power department this year will increase by 20% compared to last year? (Revenue = Electricity consumption × (Actual electricity price - Cost price))

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