
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 polar coordinate system, given the circle $C: \rho = 2\cos \left( \theta + \frac{\pi}{2} \right)$ and the line $l: \rho\sin \left( \theta + \frac{\pi}{4} \right) = \sqrt{2}$, let point $M$ be a moving point on circle $C$. Find the maximum distance from point $M$ to line $l$.

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