
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
Signals are received by an indicator from two devices, with the reception of each signal being equally likely at any moment within a time interval of duration \( T \). The moments of signal receipt are independent of each other. The indicator is triggered if the difference between the moments of signal receipt is less than \( t \) (where \( t < T \)). Find the probability that the indicator is triggered within time \( T \) if each device sends one signal.

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