
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 student passes through three intersections with traffic lights, labeled \\(A\\), \\(B\\), and \\(C\\), on the way to school. It is known that the probabilities of encountering a red light at intersections \\(A\\), \\(B\\), and \\(C\\) are \\( \dfrac {1}{3} \\), \\( \dfrac {1}{4} \\), and \\( \dfrac {3}{4} \\) respectively. The time spent waiting at a red light at these intersections is \\(40\\) seconds, \\(20\\) seconds, and \\(80\\) seconds, respectively. Additionally, whether or not the student encounters a red light at each intersection is independent of the other intersections.  
\\((1)\\) Calculate the probability that the student encounters a red light for the first time at the third intersection on the way to school;  
\\((2)\\) Calculate the total time the student spends waiting at red lights on the way to school.

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