
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 reservoir has 400 tons of water. At midnight each day, the inlet and outlet gates are opened simultaneously. The amount of water $w$ (tons) flowing out through the outlet gate is a function of time $t$ (hours): $w = 120 \sqrt{6t} \text{ for } (0 \leq t \leq 24)$.

(1) In order to ensure that the reservoir still contains 400 tons of water by midnight the next day, how many tons of water need to be added to the reservoir per hour (assuming the rate of inflow is constant each hour)?

(2) Under the conditions of part (1), at what time of day will the amount of water in the reservoir be at its minimum, and how many tons of water will be in the reservoir at that time?

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