
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
Mr. Zhang drives to work and has two routes, Route (1) and Route (2), to choose from.

Route (1): Along the way, there are two independent traffic lights, A and B. The probabilities of encountering a green light at A and B are $\frac{1}{2}$ and $\frac{2}{3}$ respectively. If a red or yellow light is encountered at A, it will cause a delay of 2 minutes. If a red or yellow light is encountered at B, it will cause a delay of 3 minutes. If green lights are encountered at both locations, the total time taken is 20 minutes.

Route (2): Along the way, there are two independent traffic lights, a and b. The probabilities of encountering a green light at a and b are $\frac{3}{4}$ and $\frac{2}{5}$ respectively. If a red or yellow light is encountered at a, it will cause a delay of 8 minutes. If a red or yellow light is encountered at b, it will cause a delay of 5 minutes. If green lights are encountered at both locations, the total time taken is 15 minutes.

(1) If Mr. Zhang chooses Route (1), what is the probability that he can reach the school in 20 minutes?

(2) In order to minimize the time Mr. Zhang spends commuting to work daily, which route would you recommend? Please explain your reasoning.

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