
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 equations of curve $C_1$ are given by $\begin{cases} x=4\cos \theta \\ y=3\sin \theta \end{cases}$ ($\theta$ is the parameter), and the polar coordinate equation of curve $C_2$ with the origin as the pole and the positive semi-axis of $x$ as the polar axis is $\rho \cos (\theta - \frac{\pi }{4})=\sqrt{2}$.

(1) Find the Cartesian equation of curve $C_2$.

(2) Find the maximum distance from a point on curve $C_1$ to curve $C_2$.

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