
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 self-driving tour group from Yichang No.1 Middle School organized a trip to the Three Gorges Dam. The group consisted of 31 cars of the same model, each with a length of approximately 5m. During the journey, they passed through a tunnel with a length of 2725m at a constant speed, with the maximum speed through the tunnel being 25m/s. Let x represent the speed of the car group. For safety and traffic flow considerations, when 0 < x ≤ 12, a distance of 20m is maintained between adjacent cars; when 12 < x ≤ 25, a distance of (1/6)x^2 + (1/3)x meters is maintained between adjacent cars. Let y represent the time from when the first car enters the tunnel to when the last car leaves the tunnel.

1. Express y as a function of x.
2. Find the minimum time y for the car group to pass through the tunnel and the corresponding speed of the car group at that time.

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