
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 long highway intersects with Narrow Street and Quiet Street (see diagram). There are traffic lights at both intersections. The first traffic light allows travel on the highway for $x$ seconds and on Narrow Street for half a minute. The second traffic light allows travel on the highway for two minutes and on Quiet Street for $x$ seconds. The traffic lights operate independently of each other. For which value of $x$ is the probability of traveling through both intersections on the Long Highway without stopping at the traffic lights the highest? What is this maximum probability?

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