
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 solid in the form of a right circular cone is 6 inches tall with a base radius of 5 inches. Two parallel planes, both parallel to the base, cut the cone, creating two frustum-shaped solids $F_1$ and $F_2$ and a smaller cone $C$ at the top. The two planes are positioned such that the volume ratio between the two frustums $F_1$ and $F_2$ is given by $\frac{F_1}{F_2} = \frac{1}{2}$. If the height of the small cone $C$ is 2 inches, find the height of frustum $F_2$.

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