
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 maze has three passages, and each person entering the maze must go through an intelligent gate. The first time you reach this gate, the system will randomly open a passage for you. If it is Passage 1, it takes 1 hour to get out of the maze; if it is Passage 2 or 3, it takes 2 hours and 3 hours, respectively, to return to the intelligent gate. Upon reaching the intelligent gate again, the system will randomly open a passage you have not used before, until you exit the maze.
(1) Calculate the probability of taking exactly 1 hour to exit the maze;
(2) Calculate the probability that the time to exit the maze exceeds 3 hours.

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