
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
The village of Li Zhuang offers two different pricing plans for electricity to its residents:
Plan A: A monthly management fee of 2 yuan per household, with electricity usage up to 30 kWh charged at 0.5 yuan per kWh and the excess charged at 0.6 yuan per kWh.
Plan B: No management fee, with electricity charged at 0.58 yuan per kWh.
(1) Determine the functional relationship $L(x)$ (in yuan) for the cost of electricity under Plan A with respect to the usage $x$ (in kWh).
(2) If Li Gang's family paid 35 yuan for their electricity in September under Plan A, how much electricity (in kWh) did they use?
(3) Within what range of monthly electricity usage (in kWh) would it be better for Li Gang's family to choose Plan A over Plan B?

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