
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
Three cars $A$, $B$, and $C$ are on a highway. $A$ and $B$ are moving in the same direction with $A$ initially behind $B$ but moving faster. $A$ needs to overtake $B$. $A$ and $C$ are moving towards each other from opposite directions. Initially, $A$ is traveling at a speed of 65 mph, $B$ is traveling at 50 mph, and $C$ at 70 mph. The distance between $A$ and $B$ is 50 feet, and between $A$ and $C$ is 300 feet. Calculate the minimum speed increase needed for $A$ to overtake $B$ safely before needing to return to the initial speed to avoid decreasing the safety distance to $C$ below 100 feet after the overtake.
A) 10 mph
B) 15 mph
C) 20 mph
D) 25 mph

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