
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
There is an opaque bag containing 4 identical balls labeled with the numbers 1, 2, 3, and 4.
(Ⅰ) If balls are drawn one by one without replacement twice, calculate the probability that the first ball drawn has an even number and the sum of the two balls’ numbers is divisible by 3.
(Ⅱ) If a ball is randomly taken from the bag and labeled as a, then put back into the bag, followed by randomly taking another ball, labeled as b, calculate the probability that the line $ax + by + 1 = 0$ has no common points with the circle $x^2 + y^2 = \frac{1}{16}$.

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