
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
**(This question is worth 12 points)**  
To ensure safe production, a factory organizes a skill test for its workers at the beginning of each month. Workers A and B have probabilities of passing each test of $p$ and $q$, respectively. Assume that whether one passes the test does not affect the other.  
(Ⅰ) Calculate the probability that worker A fails the skill test at least once in three consecutive months.  
(Ⅱ) The factory has a rule: if a worker fails the test twice in a row, they will be disqualified from their position. Calculate the probability that worker B is disqualified after exactly four tests.

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