
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 highway, Dolgoe, intersects with Uzka Street and Tikhaya Street. At both intersections, there are traffic lights. The first traffic light allows traffic on the highway for $x$ seconds and on Uzka Street for half a minute. The second traffic light allows traffic on the highway for two minutes and on Tikhaya Street for $x$ seconds. The traffic lights operate independently of each other. For what value of $x$ will the probability of driving through both intersections on Dolgoe highway without stopping at the traffic lights be the highest? What is this maximum probability?

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