
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
Given the definition: $min\{a,b\} = \begin{cases} a,\quad a\leqslant b \\ b,\quad a > b \end{cases}$. If a point $P(x,y)$ is randomly selected within the region defined by $\begin{cases} 0\leqslant x\leqslant 2 \\ 0\leqslant y\leqslant 6 \end{cases}$, find the probability that $x$ and $y$ satisfy $min\{3x-2y+6,x-y+4\}=x-y+4$.

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