
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
In the plane region defined by $\begin{cases}x\geqslant 0 \\ y\geqslant 0 \\ 4x+3y-12\leqslant 0\end{cases}$, there is a circle. When randomly placing points into this region, the circle that maximizes the probability of points falling inside it is denoted as $\odot M$. The equation of $\odot M$ is ______________.

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