
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 parametric equation of line $l$ is 
$$
\begin{cases} 
x= \frac { \sqrt {2}}{2}t \\ 
y= \frac { \sqrt {2}}{2}t+4 \sqrt {2}
\end{cases}
$$
(where $t$ is the parameter), and the polar equation of circle $c$ is $\rho=2\cos(\theta+ \frac{\pi}{4})$. Tangent lines are drawn from the points on the line to the circle; find the minimum length of these tangent lines.

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