
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 a Cartesian coordinate plane, an polar coordinate system is established with the origin O as the pole and the non-negative half-axis of the x-axis as the polar axis. The polar equation of line l is $\sqrt{2}\rho\cos(\theta + \frac{\pi}{4}) = 1$. The curve C is given by the parametric equations $\begin{cases} x=1+ \sqrt{3}\cos\alpha \\ y=\sin\alpha \end{cases}$ (with $\alpha$ as the parameter). Let point M be a moving point on the curve C, then the maximum distance from point M to line l is ______.

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