
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
A certain city has implemented a tiered electricity pricing system for residents' daily electricity usage: the first tier is for monthly electricity usage up to 170 kWh (inclusive), priced at $0.52 per kWh; the second tier is for monthly electricity usage from 171 kWh to 260 kWh, with the excess beyond the first tier priced at $0.57 per kWh; the third tier is for monthly electricity usage exceeding 260 kWh, with the excess beyond the second tier priced at $0.82 per kWh.

$(1)$ If Xiaoming's household used 160 kWh of electricity in May, what is the electricity bill for May for Xiaoming's household? ______ yuan;<br/>$(2)$ If Xiaoming's household uses x kWh of electricity per month, calculate the electricity bill for Xiaoming's household when x falls within the second and third tiers (expressed as a formula containing x);<br/>$(3)$ If Xiaoming's household used 240 kWh of electricity in July, what is the electricity bill for July for Xiaoming's household?

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