
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 passenger can go to one of three ticket counters to get a ticket. The probabilities of going to each counter depend on their locations and are respectively \( p_{1}, p_{2}, p_{3} \). The probability that the tickets will be sold out by the time the passenger arrives at the counter is \( p_{4} \) for the first counter, \( p_{5} \) for the second counter, and \( p_{6} \) for the third counter. The passenger goes to buy a ticket. What is the probability that he will get a ticket?

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