
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 Cartesian coordinate system $xOy$, the curve $C$ is given by the parametric equations 
$$
\begin{cases}
x = t\cos \alpha \\
y = \sin \alpha 
\end{cases}
(t > 0, \alpha \text{ is a parameter}).
$$
With the origin $O$ as the pole and the positive $x$-axis as the polar axis, define a polar coordinate system with the same unit length. The line $l$ has the polar equation $\sqrt{2} \rho \sin (\theta + \frac{\pi}{4}) = 3$.

(1) When $t=1$, find the maximum distance from a point on the curve $C$ to the line $l$.

(2) If all points on the curve $C$ lie below the line $l$, find the range of the real number $t$.

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