
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
Cars P and Q start traveling from the same point. Car P travels at a constant speed, $v$. Car Q starts at twice the speed of Car P, $2v$, but it accelerates uniformly over the same distance Car P traveled at a constant rate. If Car P covers the distance in time $t$, and the acceleration of Car Q is $a$ such that its final velocity is $4v$, find the time taken by Car Q to travel the same distance.
A) $\frac{t}{3}$
B) $\frac{t}{2}$
C) $\frac{2t}{3}$
D) $t$

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