
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
This year's National Day holiday was the first major holiday after the implementation of the toll-free policy for small passenger cars on highways. A self-driving tour team named "Sirius" consists of 31 cars of the same model, each about 5 meters in length (calculated as 5 meters). The team passed through a 2725-meter long tunnel (where the speed of vehicles passing through the tunnel cannot exceed 25 m/s) at a uniform speed. Let the speed of the team be $x$ m/s. For safety and traffic flow, a distance of 20 m is maintained between two adjacent cars when $0 < x \leq 12$, and a distance of $\left(\frac {1}{6}x^{2}+ \frac {1}{3}x\right)$ m is maintained when $12 < x \leq 25$. Let $y$ (s) be the time taken from the moment the first car's front enters the tunnel to the moment the last car's rear leaves the tunnel.

(1) Express $y$ as a function of $x$.
(2) Find the minimum value of the time $y$ for the team to pass through the tunnel, and the speed of the team when this minimum is achieved.

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