
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 the parametric equations of line $l$: $\begin{cases}x=t\cos\alpha \\ y=t\sin\alpha\end{cases}$, where $t$ is the parameter, establish a polar coordinate system with the origin $O$ as the pole and the positive x-axis as the polar axis. The polar equation of curve $C$ is $\rho^2 - 2m\rho\cos\theta - 4 = 0$ (where $m > 0$).
(1) If point $M$ has rectangular coordinates $(3,3)$ and lies inside curve $C$, determine the range of the real number $m$.
(2) If $m=3$, as $\alpha$ varies, determine the range of chord lengths obtained by the intersection of line $l$ and curve $C$.

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