
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
Water flows into a container at a rate of $v = 1.2$ liters per second. At what rate does the water level rise when the water has reached half the height of the container, given that the container is in the shape of an inverted right circular cone with a vertical axis, an apex pointing downward, a height of $2.4 \mathrm{~m}$, and a radius of $1 \mathrm{~m}$ at the top?

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