
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
The distance from the center of the circle C with the parametric equations 
$$
\begin{cases}
    x = 1 + \cos\theta, \\
    y = \sin\theta
\end{cases}
$$
(where $\theta$ is the parameter) to the line $l$ with the parametric equations
$$
\begin{cases}
    x = -2\sqrt{2} + 3t, \\
    y = 1 - 3t
\end{cases}
$$
(where $t$ is the parameter) is \_\_\_\_\_\_ .

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