
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

Highway Dolgoe is intersected by Uzka Street and Tikhaya Street (see diagram). Traffic lights are present at both intersections. The first traffic light allows traffic on the highway for $x$ seconds and for half a minute on Uzka Street. The second traffic light allows traffic on the highway for two minutes and for $x$ seconds on Tikhaya Street. The traffic lights operate independently of each other. For what value of $x$ will the probability of traveling along Dolgoe Highway without stopping at either traffic light be the highest? What is this highest probability?

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