
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 electric water heater's tank is fully filled with 200 liters of water and can be used for showers when heated to a certain temperature. As water is discharged, it refills automatically. Suppose in \( t \) minutes,  \( 2t^2 \) liters of water is added, and \( 34t \) liters of water is discharged. When the amount of water in the tank reaches its minimum, water discharge must be stopped, and the tank must be refilled and reheated before it can be used again. Given that each person is allowed to use no more than 60 liters of water for a shower, how many people can the water heater supply in one continuous operation at least?

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