
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
Li Zhuang Village offers two electricity billing options for households to choose from:  
Option 1: A monthly management fee of $2 per household, with electricity usage up to 30 kWh charged at $0.5 per kWh. For usage exceeding 30 kWh, the excess is charged at $0.6 per kWh.  
Option 2: No management fee, with electricity charged at $0.58 per kWh.  
(1) Find the function relationship $L(x)$ between the billing amount in dollars and the electricity usage $x$ (in kWh) for Option 1;  
(2) Li Gang's family paid $35 in September under Option 1. How much electricity did Li Gang's family use that month?  
(3) Within what range of monthly electricity usage does Option 1 become more economical than Option 2 for Li Gang's family?

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