
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]


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The National Day holiday this year is the first major holiday after the implementation of the free toll policy for small passenger cars. There is a self-driving tour group named "Tianlangxing" consisting of 31 cars of the same model, each with a length of approximately 5m (calculated as 5m). The group passed through a tunnel with a length of 2725m (the speed limit through the tunnel is 25m/s). They maintained a uniform speed of x m/s. For safety and traffic needs, 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) m is maintained between adjacent cars. The time from the first car entering the tunnel to the last car leaving the tunnel is denoted as y (s).

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 speed of the car group at that time.

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