
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 must pass through four intersections on the way to school. The probability of encountering a red light at each intersection is assumed to be independent, with the probability being $\frac{1}{3}$ at each intersection. The time spent waiting at a red light is 2 minutes each time. What is the probability that the total time a student spends waiting due to red lights is exactly 4 minutes?

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