
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
Given the cyclist encounters red lights at each of 4 intersections with probability $\frac{1}{3}$ and the events of encountering red lights are independent, calculate the probability that the cyclist does not encounter red lights at the first two intersections and encounters the first red light at the third intersection.

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