
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
If real numbers $x,y$ satisfy ${x}^{2}+{y}^{2}\leqslant 1$, then the minimum value of $\left|2x+y-2\right|+\left|6-x-3y\right|$ is      .

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