
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 taxi driver encounters six traffic signals on his way from the hotel to the train station. Assuming that the event of hitting a red light at each traffic signal is independent and that the probability is $\frac{1}{3}$ at each signal, 
(1) Find the probability that the driver encounters a red light for the first time after passing two traffic signals; 
(2) Calculate the expectation and variance of the number of red lights the driver encounters during the trip.

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