
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 equation of circle $⊙O$ as 
$$\begin{cases} x=2\sqrt{2}\cos\theta \\ y=2\sqrt{2}\sin\theta \end{cases}$$ 
($\theta$ is the parameter), find the maximum value of the distance from a point on $⊙O$ to the line 
$$\begin{cases} x=1+t \\ y=1-t \end{cases}$$ 
($t$ is the parameter).

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