
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
To encourage people to save water, a certain place implements a tiered water pricing system (as shown in the table below):

| Level | Monthly Water Usage | Price |
|-------|----------------------|-------|
| Level 1 | Up to 20 tons (including 20 tons) | $1.6$ per ton |
| Level 2 | 20 tons to 30 tons (including 30 tons) | $2.4$ per ton for the part exceeding 20 tons |
| Level 3 | Over 30 tons | $4.8$ per ton for the part exceeding 30 tons |

$(1)$ If a user consumes 10 tons of water in a month, calculate how much money they need to pay for water that month.  
$(2)$ If a user consumes 27 tons of water in a month, calculate how much money they need to pay for water that month.  
$(3)$ If a user consumes $m$ tons of water in a month $(20 < m < 30)$, then the amount of money they need to pay for water that month is ______ yuan (expressed as an algebraic expression involving $m$).  
$(4)$ If a user consumes $m$ tons of water in a month $(m > 30)$, then the amount of money they need to pay for water that month is ______ yuan (expressed as an algebraic expression involving $m).

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