
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
In the rectangular coordinate system $(xOy)$, establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of the curve $C$ is $\rho^{2}=\frac{3}{2-\cos 2\theta}$, and the polar equation of the line $l$ is $\rho\cos(\theta+\frac{\pi}{4})=\sqrt{2}$.

(1) Find the number of intersection points of line $l$ and curve $C$.

(2) Draw a line $m$ through a point on curve $C$ such that it is parallel to line $l$, and find the maximum distance between lines $m$ and $l$.

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