
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
If \( V = gt + V_0 \) and \( S = \frac{1}{2}gt^2 + V_0t + kt^3 \), then \( t \) equals:
**A)** \( \frac{2S}{V+V_0} \)
**B)** \( \frac{2S}{V-V_0} \)
**C)** \( \frac{2S(V-V_0)}{V^2 - V_0^2} \)
**D)** \( \frac{2S(V-V_0)}{V^2 - V_0^2 + 2k(V-V_0)^2} \)
**E)** \( 2S - V \)

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