
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
Let set $A = \{(x, y) \mid y \geq |x - 1|\}$ and set $B = \{(x, y) \mid y \leq -x + 5\}$. If two dice are rolled one after the other, and the number obtained from the first die is denoted as $a$, and from the second die as $b$, then the probability that $(a, b)$ belongs to $A \cap B$ is _________.

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