
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
In order to encourage residents to conserve water, a city charges residents for domestic water use in a tiered pricing system. The table below shows part of the information of the tiered pricing table for domestic water use for each household in the city ("one household, one meter"): (Water price = tap water sales cost + sewage treatment cost)

| Tap Water Sales Price | Sewage Treatment Price |
|-----------------------|------------------------|
| Monthly Water Usage per Household | Unit Price: yuan/ton | Unit Price: yuan/ton |
| 17 tons or less | $a$ | $0.80$ |
| Exceeding 17 tons but not exceeding 30 tons | $b$ | $0.80$ |
| Exceeding 30 tons | $6.00$ | $0.80$ |

It is known that in April 2012, Xiao Wang's family used 20 tons of water and paid 66 yuan for water; in May, they used 25 tons of water and paid 91 yuan for water.
$(1)$ Find the values of $a$ and $b$.
$(2)$ If Xiao Wang's family paid 184 yuan for water in June, how many tons of water did they use in June?

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