
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 a line $l$ passes through point $P(-1, 1)$, and the tangent of its inclination angle $\alpha$ is $\frac{3}{4}$. The polar equation of circle $C$ is $\rho= \sqrt{2}\cos(\theta- \frac{\pi}{4})$.
(1) Write the parametric equation of line $l$ and convert the equation of circle $C$ into Cartesian coordinates.
(2) Find the distance from the center of circle $C$ to line $l$.

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