
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 polar equation of circle C is $\rho = 2\cos(θ + \frac{π}{4})$. The parametric equation of line l is 
$$
\begin{cases}
  x= \sqrt{2}t \\
  y= \sqrt{2}t+4\sqrt{2}
\end{cases}
$$
(where t is the parameter). A tangent is drawn from a point P on line l to circle C at the point A, find the minimum value of the length of the tangent PA.

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