
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
Two cars, $A$ and $B$, are moving on a straight line in the same direction with $B$ ahead of $A$. Another car, $C$, on the opposite side, is heading towards $A$. The speeds $V_A$, $V_B$, and $V_C$ of cars $A$, $B$, and $C$ respectively are such that $V_A > V_B$. To ensure safety, $A$ should not overtake $B$ before it safely escapes a head-on collision with $C$. If the distance between $A$ and $B$ is 50 ft, and the distance between $A$ and $C$ is 200 ft, calculate the maximum possible value of $V_A$ given $V_B = 50$ mph and $V_C = 80$ mph.
A) 70 mph
B) 75 mph
C) 80 mph
D) 84 mph

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