
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
Given the equations $V = 2gt + V_0$ and $S = \frac{1}{3}gt^2 + V_0t + Ct^3$ where $C$ is a constant, find the time $t$ in terms of the other variables.
A) $\frac{2S}{V+V_0}$
B) $\frac{2S}{V-V_0}$
C) $\frac{V-V_0}{2g}$
D) $2S - V$
E) $\frac{V^2 - V_0^3}{2Sg}$

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