
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
The train schedule in Hummut is hopelessly unreliable. Train  $A$  will enter Intersection  $X$  from the west at a random time between  $9:00$  am and  $2:30$  pm; each moment in that interval is equally likely. Train  $B$  will enter the same intersection from the north at a random time between  $9:30$  am and  $12:30$  pm, independent of Train  $A$ ; again, each moment in the interval is equally likely. If each train takes  $45$  minutes to clear the intersection, what is the probability of a collision today?

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