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

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