
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
The volume of the top portion of the water tower is equal to the volume of a sphere, which can be calculated using the formula $V = \frac{4}{3}\pi r^3$. The top portion of the real tower has a volume of 50,000 liters, so we can solve for the radius:

$\frac{4}{3}\pi r^3 = 50,000$

Simplifying, we get $r^3 = \frac{50,000 \times 3}{4\pi}$. We can now calculate the radius on the right-hand side and then take the cube root to find $r$.

Now, we want to find the volume of the top portion of Logan’s model. It is given that this sphere should have a volume of 0.2 liters. Using the same formula, we can solve for the radius:

$\frac{4}{3}\pi r^3 = 0.2$

Simplifying, we get $r^3 = \frac{0.2 \times 3}{4\pi}$. We can now calculate the radius on the right-hand side and then take the cube root to find $r$.

Now, since the sphere is a model of the top portion of the water tower, the radius of the model is proportional to the radius of the real tower. Therefore, the ratio of the radius of the model to the radius of the real tower is equal to the ratio of the volume of the model to the volume of the real tower.

$\frac{r_{model}}{r_{real}} = \frac{0.2}{50000}$

We can now equate the two expressions for the radius and solve for the height of the model:

 $\frac{r_{model}}{60} = \frac{0.2}{50000}$

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