
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 particle starts with an initial velocity $V_0$ and moves under the influence of gravity $g$ and an additional constant acceleration $a$. After a time $t$, its velocity is given by $V = gt + at + V_0$ and the displacement by $S = \frac{1}{2}(g+a)t^2 + V_0t$. Solve for $t$ in terms of $S$, $V$, $V_0$, $g$, and $a$.
**A)** $\frac{2S}{V + V_0}$
**B)** $\frac{2S}{V - V_0}$
**C)** $\frac{S}{g + a}$
**D)** $\frac{V^2 - V_0^2}{2S(g + a)}$

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