
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
During driving, a driver needs a certain amount of time to react after detecting an emergency before applying the brakes. This interval is called the reaction time. Afterward, the car will continue to cover a certain distance. This distance, from the moment an emergency is spotted until the car comes to a stop, is referred to as the "braking distance." The braking distance $s$ (in meters) is related to the vehicle's speed $v$ (in meters/second) through the following formula: $s = tv + kv^2$, where $t$ is the driver's reaction time (in seconds), and $k$ is the braking coefficient. To test how alcohol consumption affects braking distance, an institution conducted a "drunk driving" test with a particular car model. It is known that the car's braking coefficient $k = 0.1$. The reaction time $t = 0.5$ seconds was recorded for the volunteer driver prior to any alcohol consumption.  
(1) If the volunteer driver has not consumed alcohol and the car speed is 10 meters/second, then the braking distance for the car is __ meters;  
(2) After drinking a bottle of beer and waiting for half an hour, the volunteer drives at a speed of 15 meters/second. The measured braking distance is 52.5 meters. At this speed, the volunteer's reaction time is __ seconds. If the volunteer had been driving at a speed of 10 meters/second, the braking distance would have been __ meters, which is __ meters more than when not under the influence of alcohol.  
(3) If you were driving this model of car at a speed of 12 meters/second and maintained a distance of 42 to 50.4 meters from the car in front of you, in order to prevent rear-ending the vehicle ahead if it suddenly stops, your reaction time must not exceed __ seconds.

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